`int_0^2f(x)dx` where `f(x) = {2x+1; 0lt=x<1, 3x^2; 1lt=xlt=2`

int_0^9 f(x) dx, where f(x)={(sinx, if 0<=x < pi/2), (1, if pi/2 <= x < 3), (e^(x-3), if 3<=x<9):}

Evaluate int_0^3 f(x)dx , Where f(x)={(x,+,3,,,0lexle2),(3x,,,,,2lexle3):}

Evaluate: (i) \int_(-1)^1f(x)dx ,\where\, f(x)={1-2x ,xlt=0 ;1+2x ,xgt=0} , (ii)\ int_(-1)^4f(x)dx ,\where\, f(x)={2x+8,-1lt=xlt=2; 6x, 2lt=xlt=4}

int_(0)^(3)f(x)dx, where f(x)=|x|+|x-1|+|x-2|

int_(0)^(2) f(x) dx = …... , where f(x) = max {x, x^(2) } .

Evaluate: int_(-5)^(0)f(x)dx" where "f(x)=|x|+|x+2|+|x+5|

Evaluate int_0^1e^x{f(x)+f'(x)}dx where f (1)=f(0)=1

Prove that int_(0)^(2a) f(x) dx = 2int_(0)^(a) f(x) dx when f(2a -x) = f(x) and hence evaluate int_(0)^(pi) |cos x| dx .

Prove that int_-a^a f(x) dx=0 , where 'f' is an odd function. And, evaluate, int_-1^1 log[(2-x)/(2+x)] dx