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A DAS GUPTA-Properties and Application of definite Integrals-EXERCISE
- int0^pi(x dx)/(a^2cos^2x+b^2sin^2x)
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- Evaluate int0^pi(x dx)/(1+cos^2x).
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- int0^pi (xtanx)/(secx+tanx)dx
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- Prove that int(0)^(pi//2)(2logsinx-logsin2x)dx=(pi)/(2)(log2).
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- int(0)^(pi//2)(sqrt(tanx)+sqrt(cotx))dx
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- Prove that: int0^(pi//2)logsinx\ dx=\ int0^(pi//2)logcosx\ dx=-pi/2log...
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- int(0)^(pi//2)log(tanx+cotx)dx=pi(log2)
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- int(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=
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- int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)
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- Q. int0^pi(e^(cos^2x)( cos^3(2n+1) x dx, n in I
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- int(0)^(2pi) (sin 2 theta)/(a-b cos 2 theta )d theta =
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- Evaluate int0^1 log(1+x)/(1+x^2)dx
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- Prove that: y=int(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int(1/8)^(cos^2x)cos^...
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- Evaluate the following: int0^(pi/2) |cosx-sinx|dx
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- Evaluate the following:int-2^2(|x|+|x-1|)dx
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- Prove that inta^b{[x]+[-x]}dx=a-b,where [x]is the greatest integer lex...
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- Statement-I int0^9[sqrtx]dx=13, Statement-II int0^(n^2) [sqrt x]dx=(n(...
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- Show that: int0^x[x]dx=[x]([x]-1)/2+[x](x-[x]), where [x] denotes the ...
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- The value of the integral overset(100pi)underset(0)int sqrt(1-cos2x)" ...
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- Evaluate the following : int(0)^(pi)(dx)/(1+sinx)
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