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Evaluate the following integrals: (a) ...

Evaluate the following integrals:
(a) `int x^8 dx`
(b) `int_2^5 x^2 dx`
(c ) `int (x+sin x) dx`

Text Solution

Verified by Experts

(a) Using formula `int x^n dx = x/(n+1), int x^8 dx = x^9/9`
(b) Using Eq. (2.44), `int_2^5 x^2 dx = x^3/3 |_2^5 =5^3/3 - 2^3/3 =(125-8)/3 =117/3`
(c ) Using Eq.(2.45), `int(f_1(x)+f_2(x)dx=int f_1(x)dx + int f_2 (x)dx and int sin x dx = cos x, " we get " int (x+sin x) dx`
`int x dx + int sin x dx = x^2/2 + cos x`
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