Evaluate the integrals in Exercises 1 to 8 using substitution.
Ex 7.10 Class 12 Maths Question 1.
Solution:
Let x² + 1 = t
⇒2xdx = dt
when
Ex 7.10 Class 12 Maths Question 2.
Solution:
put sinφ = t,so that cosφdφ = dt
Ex 7.10 Class 12 Maths Question 3.
Solution:
let x = tanθ =>dx = sec²θ dθ
when x = 0 => θ = 0
and when x = 1 =>
Ex 7.10 Class 12 Maths Question 4.
Solution:
let x+2 = t =>dx = dt
when x = 0,t = 2 and when x = 2, t = 4
Ex 7.10 Class 12 Maths Question 5.
Solution:
put cosx = t
so that -sinx dx = dt
when x = 0, t = 1; when , t = 0
Ex 7.10 Class 12 Maths Question 6.
Solution:
Ex 7.10 Class 12 Maths Question 7.
Solution:
Ex 7.10 Class 12 Maths Question 8.
Solution:
let 2x = t ⇒ 2dx = dt
when x = 1, t = 2 and when x = 2, t = 4
Choose the correct answer in Exercises 9 and 10
Ex 7.10 Class 12 Maths Question 9.
The value of integral is
(a) 6
(b) 0
(c) 3
(d) 4
Solution:
(a) let I =
Ex 7.10 Class 12 Maths Question 10.
(a) cosx+xsinx
(b) xsinx
(c) xcosx
(d) sinx+xcosx
Solution:
(b)
=-x cox+sinx
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