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Evaluate: int0^(pi//2)(acos^2x+bsin^2x)d...

Evaluate: `int_0^(pi//2)(acos^2x+bsin^2x)dx`

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USHA PUBLICATION-INTEGRATION AREA UNDER PLANE CURVES DIFFERENTIAL EQUATION -EXERCISE
  1. Evaluate int (dx)/((x+1)sqrt(1-x^2))

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  2. Evaluate :int0^(pi//2)sin^4tdt

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  3. Evaluate: int0^(pi//2)(acos^2x+bsin^2x)dx

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  4. Evaluate: int(pi//4)^(pi//2)costheta.cosec^2theta d theta

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  5. int1/((x+1)(x+2))dx

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  6. Evaluate int(0)^(pi//2)(cos^(5)x)/(sin^(5)x+cos^(5)x)dx.

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  7. Find the area of the region enclosed by x=1+y^2,X=0,y=3,y=6

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  8. Find the area of the region enclosed by y^2=4x,X=0,y=0,y=4

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  9. Find the area of the region enclosed by y^2=x,x=0,y=2

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  10. Solve the following differential equation:dy/dx+(2x)/(1+x^2)y=(x^3)/(1...

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  11. Solve the following differential equation :(1+y^2)dx=(tan^-1y-x)dy

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  12. Solve the following differential equation:x(dy)/(dx)+y^2/x=y

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  13. Solve the following differential equation:x(dy)/(dx)+y^2/x=y

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  14. Write the degree of differential equation:(d^2y)/dx^2+3(dy/dx)^2=xlog(...

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  15. Find the equation of a curve passing through the point(0,-2),given th...

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  16. Solve each of the following differential equations : x cos y""dy= (x...

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  17. If dy/dx=-y^2/100and y(0)=15,find the value of x when y=10.

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  18. If (dT)/dt=-K(T-S)where K and S are constants,find T when T(0)=100.

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  19. If (dC)/dx=2+0.15xfind C(x)given that C(0)=150.

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  20. Evaluate: int (x^2)/(x^4+x^2+1) dx

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