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CHHAYA PUBLICATION-DEFINITE INTEGRAL -EXERCISE 9B (VERY SHORT ANSWER TYPE QUESTIONS)
- If f(2a-x)=-f(x), then show that, int(0)^(2a)f(x)dx=0
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- If f(x) is an odd function of x, then show that, int(-a)^(a)f(x)dx=0.
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- Evaluate : int(-1)^(1)|x|dx
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- Evaluate : int(-(pi)/(2))^((pi)/(2))|sinx|dx
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- Evaluate : int(1)^(3)|x-2|dx
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- Prove that, int(0)^(pi)f(sinx)dx=2int(0)^((pi)/(2))f(sinx)dx.
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- Show that, int(0)^(pi)xf(sinx)dx=(pi)/(2)int(0)^(pi)f(sinx)dx.
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- Show : int(a)^(b)f(kx)dx=(1)/(k)int(ka)^(kb)f(x)dx
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- Show : int(0)^((pi)/(2))sinxf(sin2x)dx=int(0)^((pi)/(2))cosxf(sin2x)...
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- Prove that, int(a)^(b)f(a+b-x)dx=int(a)^(b)f(x)dx.
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- int(0)^(pi)cos^(5)xdx=0
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- int(0)^(8pi)sin^(6)xdx=8int(0)^(pi)sin^(6)xdx
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- int(-a)^(a)(xe^(x^(4)))/(1+x^(2))dx=0
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- int(0)^(pi)sin^(3)xcos^(7)xdx=0
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- int(-(pi)/(2))^((pi)/(2))sin^(7)xdx=0
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- int(0)^(pi)(sin4theta)/(sintheta)d theta=0
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- int(0)^((pi)/(2))log(tanx)dx=0
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- int(0)^(2pi)sin^(4).(x)/(2)cos^(5).(x)/(2)dx=0
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- int(-a)^(a)xsqrt(a^(2)-x^(2))dx=0
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- int(-1)^(1)sin^(-1).(2x)/(1+x^(2))dx=0
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