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CHHAYA PUBLICATION-DEFINITE INTEGRAL -EXERCISE 9B ( SHORT ANSWER TYPE QUESTIONS )
- Show that, int(0)^(pi)sin^(4)xdx=2int(0)^((pi)/(2))sin^(4)xdx, hence, ...
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- Prove that, int(-(pi)/(2))^((pi)/(2))cos^(3)xdx=2int(0)^((pi)/(2))cos^...
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- int(0)^((pi)/(2))(sinx)/(sinx+cosx)dx
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- int(0)^((pi)/(2))(sqrt(sinx)dx)/(sqrt(sinx)+sqrtcosx)
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- int(0)^(pi)xcos^(2)xdx
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- int(0)^(pi)(xdx)/(1+sinx)
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- int(0)^((pi)/(2))(cosx-sinx)/(1+sinxcosx)dx
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- int(0)^((pi)/(2))(sqrt(cotx)dx)/(sqrt(cotx)+sqrt(tanx))
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- int(0)^((pi)/(2))(acos^(2)x+bsin^(2)x)dx
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- int(0)^((pi)/(2))(sin^(3)theta)/(sin^(3)theta+cos^(3)theta)d theta
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- int(-(pi)/(2))^((pi)/(2))(dx)/(1+cot^(4)x)
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- int(0)^(pi)(e^(cosx)dx)/(e^(cosx)+e^(-cosx))
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- int(0)^((pi)/(2))(sin^((3)/(2))x)/(sin^((3)/(2))x+cos^((3)/(2))x)dx
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- int(0)^((pi)/(2))(sin^(4)x)/(sin^(4)x+cos^(4)x)dx
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- Prove that: int(-1)^(1)x|x|dx=0
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- Prove that: int(-2)^(2)|1-x^(2)|dx=4
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