7. Show that log(1+x) dx = log2 2 1+x dx 8. Use Gamma function to prove...

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7. Show that log(1+x) dx = log2 2 1+x dx 8. Use Gamma function to prove that 0 (1-x)6 3 22 9. Find the area of two loops of the curve ay = ax-x4 OR Find the volume of the solid formed by the revolution of the cycloid xa (0+sin0), y=a (1-cos 0) about the tangent at the vertex. 7. Show that log(1+x) dx = log2 2 1+x dx 8. Use Gamma function to prove that 0 (1-x)6 3 22 9. Find the area of two loops of the curve ay = ax-x4 OR Find the volume of the solid formed by the revolution of the cycloid xa (0+sin0), y=a (1-cos 0) about the tangent at the vertex.