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JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q.1. What is JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced equal to?
(a) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(b) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(c) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(d) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (c)
Given,
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Computing I1,
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Put sin x = t → cos x dx = dt
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Similarly,
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Put cos x = t → - sin x dx = dt
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Putting these value in I,
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
∴ The correct answer is option (C).

Q.2. If (x) = ekx; then find the indefinite integral of f (x)?
(a) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(b) ex + c
(c) -e-x + c
(d) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (a)
Integration of ekx
Integrating f (x) = ekx with respect to dx.
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
= JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
where 'c' is the constant,

Q.3. JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanceddx is equal to
(a) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(b) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(c) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(d) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced

Correct Answer is option (c)
The Given Question is Wrong, Marks are allotted to all.
Given that, JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
option 1-
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
option 2-
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
option 3-
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
option 4-
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced

Q.4. The value of JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced, where dA indicate small area in xy-plane, is
(a) 1/2 sq. units
(b) 1/3 sq. units
(c) -1/2 sq. units
(d) -1/3 sq. units

Correct Answer is option (b)
Given:
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
= 1/3

Q.5. Evaluate JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(a) esinx + c
(b) 2esin-1x + c
(c) esin-1x + c
(d) esin-1x + 2c

Correct Answer is option (c)
Given Integral
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Let, JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced as we know the derivative of JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Now the equation reduces to
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced ⇒ we know ∫exdx = ex + c  
∴ ∫ etdt = et + c, as t = sin-1 x our equation becomes esin-1x  + c 
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced

Q.6. Consider the following definite integral:
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
The value of the integral is
(a) π3/24
(b) π3/12
(c) π3/48
(d) π3/64

Correct Answer is option (a)
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Put sin-1 x = t 
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
= JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
= JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
= π3/24

Q.7. Let x be a continuous variable defined over the interval (-∞, ∞) and  JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced. The integral g(x)=∫f(x)dx  is equal to 
(a) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(b) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(c) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(d) e-x

Correct Answer is option (b)
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Substitude e-x = t 
-e-x dx = dt 
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced

Q.8. JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced =
(a) 1/3
(b) 1/2
(c) -1/2
(d) -1/3

Correct Answer is option (b)
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
Let, t = x2 ⇒ dt = 2xdx ⇒ xdx = dt/2 
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
= JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
I = 1/2

Q.9. The value of JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced is
(a) -1/2
(b) 13/10
(c) 1/2
(d) 28/10

Correct Answer is option (b)
For Integration with modulus, first we have to find the point where the sign of the value of the function gets change.
Given:
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
f(x) = 5x - 3 = 0
x = 3/5
∴ from 0 to 3/5 the function is negative and 3/5 to 1 the function is positive.
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced

Q.10. JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced is equal to
(a) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(b) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(c) JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced
(d) None of these

Correct Answer is option (b)
Let,
I = ∫ex{f(x)  +f′(x)}dx
= ∫ex f(x)dx + ∫ex f′(x)dx + C
By solving through integration by parts, we get
= {ex f(x) − ∫f′(x)ex dx} + ∫ex f′(x)dx + C
= f(x).ex + C
where C is constant

The document JEE Advanced (Single Correct Type): Indefinite Integral | Chapter-wise Tests for JEE Main & Advanced is a part of the JEE Course Chapter-wise Tests for JEE Main & Advanced.
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