7. Apply the method of differentiation under integral sign to prove: x/2 dx (a sin x+b...

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7. Apply the method of differentiation under integral sign to prove: x/2 dx (a sin x+b cos x) (a +b) 4a3b3 i 8. Use Gamma function to prove that (- dx 1/6 o (1-x) 3 9. Find the area bounded by the curve xy = a(a-y) and the x axis. OR Find the volume of the solid formed by revolving the cycloid x ( + sine), ya(1+cose) about its base. 10. Solve the differential equation: (1 + y) + (x etany) 11. Solve: xy (p+2)=2py +x dy=0. dx 7. Apply the method of differentiation under integral sign to prove: x/2 dx (a sin x+b cos x) (a +b) 4a3b3 i 8. Use Gamma function to prove that (- dx 1/6 o (1-x) 3 9. Find the area bounded by the curve xy = a(a-y) and the x axis. OR Find the volume of the solid formed by revolving the cycloid x ( + sine), ya(1+cose) about its base. 10. Solve the differential equation: (1 + y) + (x etany) 11. Solve: xy (p+2)=2py +x dy=0. dx