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int(0)^(-pi//2)sin^(5)xcos^(4)xdx...

`int_(0)^(-pi//2)sin^(5)xcos^(4)xdx`

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Evaluate int_(0)^(pi)sin^(3)x*cos^(4)xdx

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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Self practive problem
  1. Evaluate int(0)^(pi)ln(1+bcosx) dx, 'b' being parameter.

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  2. int(pi//2)^(0)sin^(11)xdx

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  3. int(0)^(-pi//2)sin^(5)xcos^(4)xdx

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  4. int(0)^(1) x^(5)sin^(-1)xdx

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  5. int(0)^(9) x(a^(2)-x^(2))^(7/2)dx

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  6. int(0)^(2) sqrt(2-x)dx.

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  7. Prove the following : int(0)^(1)e^(-x)cos^(2)xdx lt int(0)^(1)e^(-x^(2...

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  8. Prove the following : 0 lt int(0)^(pi//2)sin^(n+1)xdx lt int(0)^(pi//2...

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  9. Prove the following : e^(-(1)/(e)) lt int(0)^(1)x^(x)dx lt 1

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  10. Prove the following: -1/2lt=int0^1(x^3cosx)/(2+x^2)dx<1/2

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  11. Prove the following : 1 lt int(0)^(pi//2)sqrt(sinx)dx lt sqrt(pi/2)

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  12. Prove the following : 4/pi lt int(pi/4)^(pi/3) (tanx)/(x) lt (3sqrt(3)...

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  13. lim(nrarroo) {1/n+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+"......"+1/(...

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  14. lim(nrarroo) [1/(1+n)+(1)/(2+n)+(1)/(3+n)+"....."+(1)/(5n)]

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  15. lim(nrarroo) [sin^(3)'(pi)/(4n)+2sin^(3)'(2pi)/(4n)+3sin^(3)'(3pi)/(4n...

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  16. lim(nrarroo) sum(r=0)^(n-1) (1)/(sqrt(n^(2)-r^(2)))

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  17. lim(nrarroo) (tan'(pi)/(2n)tan'(2pi)/(2n)tan'(3n)/(2n)"......."tan'(np...

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  18. Find the area bounded by the curves y = e^(x), y = |x-1| and x = 2.

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  19. Complete the area of the region bounded by the parabolas y^(2)+8x=16 ...

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  20. Find the area between the x-axis and the curve y = sqrt(1+cos4x), 0 ...

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