1. (s-10) By using substitution solve the following lodefinite integrate (a) (b) int (x^3dx)/(sqrt [3](2+x^4)) (c) int xcosx^2dx int (dx)/(sqrt (x)(1-sqrt (x))^3) 2. (s-10) By using substitution solve the following definite integrals. (a) int _(0)^1(xdx)/(sqrt [3](1+x^2)) (b) int _(0)^(pi )/(2)(cosxdx)/(sqrt (2+sinx)) 3. (S-15) By using definite integral find area of the following region enclosed by the parabola y_(1)=x^2+2x+2 and the line y_(2)=4x+5 4. (S-15) The region bounded by the curve y_(1)=x^2-2x and the line y_(2)=2x+5 is revolved about the r-axis to generate a solid. By using definite integral (Washer Method) find the volume of the solid. 5. (S-15) Find the length of the following plane curve defined by: x=sin^2t y=cos^2t,0leqslant tleqslant (pi )/(4) 6. By using integration by parts evaluate the integrals: int x^(1)/(3)lnxdx,int x^2cosxdx 7. (S-15) By using integration by part and functional equation evaluate the integrals int e^2xcos3xdx (S-10) By using integration of rational functions evalute the integral int (x^3-2x^2+x+3)/(x^2)-4x+3dx

1. (a) Let , then , and .Substitute and into the integral: (b) Let , then , and .Substitute and into the integral: (c) Let , then , and .Substitute and into the integral: 2. (a) Let , then , and .Substitute and into the integral: (b) Let , then , and .Substitute and into the integral: 3. The area enclosed by the parabola and the line is given by the integral:$\int_{-\in