Giải bài 4.43 trang 21

Đề bài

a) $\underset{0}{\overset{3}{\int }}\left|3-x\right|dx$;

b) $\underset{0}{\overset{2}{\int }}\left(e^x-4x^3\right)dx$

c) $\underset{0}{\overset{\frac{\pi }{2}}{\int }}\left(\sin x+\cos x\right)dx$.

Lời giải chi tiết

a) Ta có $\left|3-x\right|=3-x$ với $x\in \left[0;3\right]$.

Suy ra $\underset{0}{\overset{3}{\int }}\left|3-x\right|dx=\underset{0}{\overset{3}{\int }}\left(3-x\right)dx={\left(3x-\frac{x^2}{2}\right)|}_0^3=9-\frac{9}{2}=\frac{9}{2}$.

b) Ta có $\underset{0}{\overset{2}{\int }}\left(e^x-4x^3\right)dx={\left(e^x-x^4\right)|}_0^2=e^2-2^4-1=e^2-17$.

c) $\underset{0}{\overset{\frac{\pi }{2}}{\int }}\left(\sin x+\cos x\right)dx={\left(-\cos x+\sin x\right)|}_0^{\frac{\pi }{2}}=1+1=2$.