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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) eax cos bx
(ii) e2x sin x
(iii) e-x cos 2x
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 1
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 2
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 3

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

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 4
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 5

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

Question 1.
e2x sin 3x dx
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 6
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 7
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 8

Question 2.
ex cos 2x
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 9
Substituting (2) in (1) we get,
I = ex cos 2x + [ex + sin 2x – 2I]
I = ex cos 2x + 2ex sin 2x – 4I
5I = ex(cos 2x + 2 sin 2x)
∴ I = \(\frac{e^{x}}{5}\)[cos 2x + 2 sin 2x] + c

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

Question 3.
e3x sin 2x
Solution:
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 10
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 11
Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.8 12

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