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Using properties evaluate the following ...

Using properties evaluate the following definite integrals,
evaluate the following: `int_(-pi/2)^(pi/2) sin^2x dx`

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`sin^2(-x) = (-sinx)^2 = sin^2x`
therefore `sin^2x` is an even function
therefore `int_(-pi/2)^(pi/2) sin^2 x dx = 2int_0^(pi/2) sin^2x dx`
=`2 int_0^(pi/2) (1-cos 2x)/2 dx`
=`[x-(sin2x)/2]_0^(pi/2)`
`(pi/2 -sinpi/2) -(0-sin0/2) = pi/2`
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A N EXCEL PUBLICATION-INTEGRALS-QUESTION BANK
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  2. Using properties evaluate the following definite integrals, evaluate ...

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  5. Evaluate the following: int(-pi/2)^(pi/2)sin^7xdx

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  15. Evaluate int(pi/6)^(pi/3) dx/(1+sqrttanx)

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  16. Find int0^(pi/2) logsinxdx

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  18. Integrate the following functions w.r.t.x cosx/sqrt(4-sin^2x)

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  19. Integrate the following functions x^3/sqrt(1-x^8)

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  20. integrate the following functions e^x/((1+e^x)(2+e^x))

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