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

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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: