Question

Tính các tích phân sau :

a) \(\int\limits^{\dfrac{1}{2}}_{-\dfrac{1}{2}}\sqrt[3]{\left(1-x\right)^2dx}\)

b) \(\int\limits^{\dfrac{\pi}{2}}_0\sin\left(\dfrac{\pi}{4}-x\right)dx\)

c) \(\int\limits^2_{\dfrac{1}{2}}\dfrac{1}{x\left(x+1\right)}dx\)

d) \(\int\limits^2_0x\left(x+1\right)^2dx\)

e) \(\int\limits^2_{\dfrac{1}{2}}\dfrac{1-3x}{\left(x+1\right)^2}dx\)

g) \(\int\limits^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}}\sin3x\cos5xdx\)

Answer 1

a) =

=

b) = =

=

c)=

d)=

=

e)=

=

g)Ta có f(x) = sin3xcos5x là hàm số lẻ.

Vì f(-x) = sin(-3x)cos(-5x) = -sin3xcos5x = f(-x) nên: