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Integral Calculus

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14 Mar 2010 10:27:58 IST

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Solve Integral?

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Solve the integral using properties of integrals .sinx + cosx / 9 + 16sin2x dx

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Deepak Aggarwal

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Joined: 9 May 2009

Posts: 766

15 Mar 2010 16:31:22 IST

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I = int x from 0 to pi/4 (sinx + cosx)dx / (9 + 16sin2x)

I = int x from 0 to pi/4(sinx + cosx)dx / (25 - 16(sinx - cosx)²)

Put y = sinx - cosx

or, dy = (cosx + sinx).dx

When x = 0, y = -1 and when x = pi/4 , y = 0

I = int y from -1 to 0 (dy / 25 - 16y²)

I = (1/16) int y from -1 to 0 ( dy/ (5/4)² - y² )

I = (1/16) (2/5) |log(5 + 4y / 5 - 4y)| with limit of y from -1 to 0

I = (1/40) ( 0 - log(1/9) )

I = (1/40) (log9)

Himanshu Garg

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Joined: 8 Jul 2008

Posts: 40

15 Mar 2010 17:14:10 IST

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Using properties of integrals we have to solve

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