INTEGRATION USING TRIGONOMETRIC AND HYPERBOLIC SUBSTITUTIONS 407H
Hence∫ 32√
(x^2 −4) dx=[
3
2√
5 −2(0.9624)]
−[0]= 1. 429 , correct to 4 significant figuresNow try the following exercise.
Exercise 162 Further problems on integra-
tion using the coshθsubstitution- Find
∫
1
√
(t^2 −16)dt[
cosh−^1x
4+c]- Find
∫
3
√
(4x^2 −9)dx[
3
2cosh−^12 x
3+c]- Find
∫ √
(θ^2 −9) dθ
[
θ
2√
(θ^2 −9)−9
2cosh−^1θ
3+c]- Find
∫ √
(4θ^2 −25) dθ[θ√(θ^2 −25
4)
−25
4cosh−^12 θ
5+c]- Evaluate
∫ 212
√
(x^2 −1)dx [2.634]- Evaluate
∫ 32√
(t^2 −4) dt [1.429]