" 1."int_(a)^(b)xdxquad " 2."int_(0)^(5)(x

int_(1)^(2)xdx

int_(0)^(1)2xdx

If int_(a)^(b)|sin x|dx=8 and int_(0)^(a+b)|cos x|dx=9 then find the value of int_(a)^(b)x sin xdx

Prove that int_(-a)^(a) dx = {(2int_(0)^(a) f(x) dx, if f(x) "is even"),(0, if f(x) "is odd"):} and hence evaluate (a) int_(-1)^(1) sin^(5)x cos^(4)xdx .

int_(0)^(1)log xdx

Show that int_(0)^(2)(2x+1)dx = int_(0)^(5)(2x+1)+int_(5)^(2)(2x+1)

Show that int_(0)^(2)(2x+1)dx = int_(0)^(5)(2x+1)+int_(5)^(2)(2x+1)

Prove that int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx and hence evaluate the following: (f) int_(0)^(pi)(xdx)/(a^(2)cos^(2)x + b^(2)sin^(2)x)

Evaluate : (i) int_(0)^(2)e^(x//2)dx (ii) int_(2)^(4)(x)/((x^(2)+1))dx (iii) int_(0)^(1)cos^(-1)xdx

Prove that int_(0)^(a) f(x) dx= int_(0)^(a) f(a-x)dx . Hence find int_(0)^((pi)/(2)) sin^(2) xdx