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# Integer Answer Type Questions: Indefinite Integral - Notes | Study All Types of Questions for JEE - JEE

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Q.1. Find the maximum area bounded by the curves y2 = 4ax, y = ax and y = x / a (1 ≤ a ≤ 2).

Ans. 84 The curves are y2 = 4ax and y = ax
At their point of intersection
a2x2 = 4ax
⇒ ax = 4, x = 0
x = 4  /  a
⇒ y = 4
i. e. Similarly for y2 = 4ax and y = x / a , ⇒ x = 4a3
⇒ B(4a3, 4a2)
Area OAB =    = 84

Q.2. Let f be a real valued function satisfying and Find the area bounded by the curve y = f(x), the y–axis and the line y = 3.

Ans. 3 Given, putting x = y =1, we get  f(1) = 0
Now, = ⇒ f'(x)  = 3 x ⇒ f(x) = 3 lnx + c
Putting x =1 ⇒ c = 0 ⇒ f(x) = 3lnx = y  (say)
Required Area = = 3(e – 0) = 3e sq. units.

Q.3. is equal to

Ans. 0
Given Limit = = Q.4. The value of ,where [.] denotes the greatest integer function, is equal to;

Ans. 12
Let I =  = 1/3 (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) = 12.

Q.5. If , then the value od P + Q + R is________.

Ans. 10
Put x + 7 = u4   ⇒ dx = 4u3 du Rearranging like terms ⇒ P = 2, Q = 4, R = 4
⇒ P + Q + R = 10.

Q.6. If ,  then k is equal   s.

Ans. 1
Dividing the numerator and denominator by  x2, the   given  integral  becomes Let Hence   k = 1.

Q.7. The value of is ____________.

Ans. 9 Q.8.  If , then where  k  has the value equal to?

Ans. 9    ⇒ k = 9

Q.9. Value of is equal to?

Ans. 1  = 1

Q.10. Let  f be a function defined by , where r = 3k, k∈ I then is equal to?

Ans. 5 Hence, f(x) is periodic with fundamental time period = 3 = 50 = 5

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## All Types of Questions for JEE

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## All Types of Questions for JEE

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