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A DAS GUPTA-Definite Integration-EXERCISE
- Evaluate intdx/(x+sqrt(1+x^2))^n,n!=+-1
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- Integrate from the first principles int0^(pi/2) sinx dx
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- int0^(pi/4)cos^2x dx
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- Evaluate int(0)^(1)x^(2)dx as the limit of a sum.
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- Integrate:int0^1 2^xdx
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- Evaluate the following integrals as limit of sum: inta^b e^x dx
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- Integrate int1^2x^3dx
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- lim(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+.....
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- Evaluate lim(nrarroo)(2)/(n)(sin.(pi)/(2n)+sin.(2pi)/(2n)+sin.(3pi)/...
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- underset(ntoinfty)lim(n/(n^2+1^2)+n/(n^2+2^2)+n/(n^2+3^2)+...+1/(2n)) ...
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- lim(n rarr oo)[(e^(1//n)+e^(2//n)+e^(3//n)+...+e^(n //n))/n]
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- lim(nrarroo)((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)...
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- underset(nto oo)lim{(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)} is, e...
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- lim(n->oo)1/n[1/(n+1)+2/(n+2)+....+(3 n)/(4 n)]
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- lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)
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- lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)
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- Evaluate intcos^5(x/2)sinxdx
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- Evaluate the following:int0^(pi/2)(sinxcosxdx)/((a^2cos^2x+b^2sin^2x)^...
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- Evaluate int0^(pi//2)(sin^2xdotcos^2x)/((sin^3x+cos^3x)^2)dx
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- Evaluate the following:int0^1xlogxdx
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- Evaluate : int1^16tan^(- 1)sqrt(sqrt(x)-1)dx
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