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## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8

Integrate the following with respect to x.

Question 1.

(i) e^{ax} cos bx

(ii) e^{2x} sin x

(iii) e^{-x} cos 2x

Solution:

Question 2.

(i) e^{-3x} sin 2x

(ii) e^{-4x} sin 2x

(iii) e^{-3x} cos x

Solution:

### Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 Additional Problems

Question 1.

e^{2x} sin 3x dx

Solution:

Question 2.

e^{x} cos 2x

Solution:

Substituting (2) in (1) we get,

I = e^{x} cos 2x + [e^{x} + sin 2x – 2I]

I = e^{x} cos 2x + 2e^{x} sin 2x – 4I

5I = e^{x}(cos 2x + 2 sin 2x)

∴ I = \(\frac{e^{x}}{5}\)[cos 2x + 2 sin 2x] + c

Question 3.

e^{3x} sin 2x

Solution: