Giải bài 63 trang 30

Đề bài

Tính:

a) $\underset{0}{\overset{1}{\int }}-2dx$;

b) $\underset{0}{\overset{1}{\int }}\frac{2x}{3}dx$;

c) $\underset{0}{\overset{1}{\int }}{x}^{4}dx$;

d) $\underset{1}{\overset{3}{\int }}2\sqrt[3]{3x}dx$;

e) $\underset{1}{\overset{2}{\int }}\frac{2}{3x}dx$;

g) $\underset{1}{\overset{9}{\int }}\left(x\sqrt{x}-2\right)dx$.

Lời giải chi tiết

a) $\underset{0}{\overset{1}{\int }}-2dx={-2x|}_0^1=-2$.

b) $\underset{0}{\overset{1}{\int }}\frac{2x}{3}dx={\frac{2}{3}.\frac{x^2}{2}|}_0^1={\frac{x^2}{3}|}_0^1=\frac{1}{3}$.

c) $\underset{0}{\overset{1}{\int }}{x}^{4}dx={\frac{x^5}{5}|}_0^1=\frac{1}{5}$.

d) $\underset{1}{\overset{3}{\int }}2\sqrt[3]{3x}dx=\underset{1}{\overset{3}{\int }}2x^{\frac{1}{3}}dx={\frac{2x^{\frac{4}{3}}}{\frac{4}{3}}|}_1^3={\frac{3x\sqrt[3]{3x}}{2}|}_1^3=\frac{9\sqrt[3]{33}-3}{2}$.

e) $\underset{1}{\overset{2}{\int }}\frac{2}{3x}dx={\frac{2}{3}\ln \left|x\right||}_1^2=\frac{2}{3}\ln 2$.

g) $\underset{1}{\overset{9}{\int }}\left(x\sqrt{x}-2\right)dx=\underset{1}{\overset{9}{\int }}\left(x^{\frac{3}{2}}-2\right)dx={\left(\frac{x^{\frac{5}{2}}}{\frac{5}{2}}-2x\right)|}_1^9$

$={\left(\frac{2x^2\sqrt{x}}{5}-2x\right)|}_1^9=\frac{396}{5}-\left(-\frac{8}{5}\right)=\frac{404}{5}$.