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A DAS GUPTA-Properties and Application of definite Integrals-EXERCISE
- Evaluate: int(-1)^(3//2)|xsinpix|dx
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- Prove that int0^(pi/2)(costheta-sintheta)/(1+sintheta.costheta)d theta...
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- Evaluate: int0^(pi/2) sin^2x/(sinx+cosx)dx
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- int(0)^(pi)log(1+cosx)dx=-pi(log2)
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- Prove that int0^(2a) f(x)/(f(x)+f(2a-x))dx=a
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- Evaluate: int0^(pi//4)"log"(1+"t a n x")dx
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- Evaluate: int0^(pi//4)(sin\ 2x)/(cos^4x+sin^4x)dx
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- Evaluate: int0^pi(xsinx)/(1+cos^2x)dx
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- Evaluate int(0)^(pi)(xdx)/(1+cosalphasinx),0ltalphaltpi.
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- 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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