`int_(0)^(1)x(1-x)^(pi)dx`

7(int_(0)^(1)(x^(4)(1-x)^(4)dx)/(1+x^(2))+pi) is equal to

show that (a) int_(0) ^(2pi) sin ^(3) x dx = 0 , (b) int_(-1)^(1) e^(-x^(2)) dx = 2 int_(0)^(1) e^(-x^(2)) dx

sum_(n=1)^(oo)(1)/(n^(2))=(pi^(2))/(6) and int_(0)^(1)(ln x)/(1-x^(2))dx=-(pi^(2))/(lambda)

int_(0)^(pi)(x)/(1+sinx)dx .

[-int_(0)^(1)sqrt(1-x)dx],[=(pi)/(2)-1]

If I=int_(0)^(1) (1)/(1+x^(pi//2))dx then

int_(0)^(1)(xe^(x)+(sin)(pi x)/(4))dx

int_(0)^(1)(xe^(x)+sin(pi(x)/(4)))dx

Show that int_(0)^(1)(dx)/(1+x^(6))>(pi)/(4)

int_(0)^(1)(cos x)/(1+x)dx=k and int_(6 pi-3)^(6 pi)(cos((x)/(3)))/(6 pi+3-x)dx=mk