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Find the following integrals. int0^(pi...

Find the following integrals.
`int_0^(pi/2)frac(sinx)(1+cos^2x)dx`

Text Solution

Verified by Experts

Put cosx = 1.
Then dt = -sinx dx
`gt sinx dx = -dt`
Also x = 0 `gt t = 1` and
x = `pi/2 gt t = 0
therefore `int_0^(pi/2) sinx/(1+cos^2 x) dx = int_1^0 (-dt)/(1+t^2)`
=`-[tan^-1 t]_1^0 = -[0-pi/4] = pi/4`
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A N EXCEL PUBLICATION-INTEGRALS-QUESTION BANK
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  3. Find the following integrals. int0^(pi/2)frac(sinx)(1+cos^2x)dx

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  4. Evaluate the following definite integrals int0^2dx/(x+4-x^2)

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  5. Evaluate the following definite integrals int-1^1 dx/(x^2+2x+5)

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  8. If f(x) = int0^x tsint dt, then find f^'(x)

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  9. int0^(pi/2)frac(sinx)(sinx+cosx)dx

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  12. Evaluate int-1^2 abs[x^3-x]dx

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  13. Evaluate int(-pi/4)^(pi/4) sin^2 x dx

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  14. Evaluate int0^pi (xsinx)/(1+cos^2x)dx

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  16. Find the following integrals. int0^(pi/2)frac(sqrtsinx)(sqrtsinx+sqr...

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  18. Using properties evaluate the following definite integrals int0^(pi/2)...

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