Answer in detail please

Problem 6. (5 pts each) Calculate each of the following three definite integrals. TT /2 (i) |x2 - Ar + 3/dx (ii) 1 sin a (1 + 7 cos4 x) 1/3 COS" x sin x dx 6x" + 1 + x2 da 3n n Problem 7. (5 pts) Evaluate the expression lim n- too n+1 Problem 8. (5 pts) If f(x) = batx7 +e, find (f-1)'(1). Problem 9. (5 pts) Use logarithmic differentiation to find the derivative of the function y = (5x + 1)20 (24 - 7)19 Problem 10. (5 pts each) Differentiate each of the following functions. (i) f(x) = sin (5x + 1) (ii) g(x) = xsing, for each r E (0, too) Problem 11. (5 pts each) Compute the following three integrals. (1) 22523 dx 1 (ii) 2 In x dx VI (1+x) (iii) dx Problem 12. (7 pts) Evaluate the following limit. t+1 cos 0 lim 1-+ 7 / 4 t -1/4 Ju/41+0 de Note that you are not allowed to use a technique that was not introduced or discussed in this course