Test: Integration By Substitution


5 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Integration By Substitution


Description
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QUESTION: 1

Solution:

cos(sin-1x)/(1-x2)½……………….(1)
t = sin-1 x
dt = dx/(1-x2)½
Put the value of dt in eq(1)
= ∫cost dt
= sint + c
= sin(sin-1 x) + c
⇒ x + c

QUESTION: 2

Integral of sin5x.cos2x is: 

Solution:

So Looking at this integral, we have



 

QUESTION: 3

Evaluate: 

Solution:

xex = t
(xex + ex) dx = dt
= ex(x + 1) dx = dt
= ∫dt/sin2t
= ∫cosec2t dt
= -cot(xex) + c

QUESTION: 4

Evaluate: 

Solution:

Create ((X+B) + (A-B)) in numerator and then apply Sin(a+b) formula then you will be able to solve it.

QUESTION: 5

Find the distance travelled by a car moving with acceleration given by a(t)=t2 + t, if it moves from t = 0 sec to t = 10 sec, if velocity of a car at t = 0sec is 40 km/hr.

Solution:





= 783.3 km

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