6. Integrate any three X.ex .a) .dx (1+x) b) f c) .dx 1+ex 4 log(1 +...

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6. Integrate any three X.ex .a) .dx (1+x) b) f c) .dx 1+ex 4 log(1 + x) 2 1+x .dx -/2 cot x .dx ! 1+cotx 7. Evaluate fxdx by the method of summation. 3. Obtain reduction formula for [cot" x dx and hence integrate fcotx dx. OR Using Gamma function show that Je-x.xdxx Je** fex.dx= 0 9. Find the area bounded by the cardioid r = a(1 + cose) OR = C 82 Find the volume of the solid formed by revolving the cycloid x ya(1+cose) about its base. = a(0 + sin), 6. Integrate any three X.ex .a) .dx (1+x) b) f c) .dx 1+ex 4 log(1 + x) 2 1+x .dx -/2 cot x .dx ! 1+cotx 7. Evaluate fxdx by the method of summation. 3. Obtain reduction formula for [cot" x dx and hence integrate fcotx dx. OR Using Gamma function show that Je-x.xdxx Je** fex.dx= 0 9. Find the area bounded by the cardioid r = a(1 + cose) OR = C 82 Find the volume of the solid formed by revolving the cycloid x ya(1+cose) about its base. = a(0 + sin),