Giải bài tập 6 trang 40

Đề bài

Tính:

a) $\underset{-1}{\overset{1}{\int }}{(x+2)}^{3}dx$

b) $\underset{1}{\overset{2}{\int }}\frac{2}{x^2}dx$

c) $\underset{1}{\overset{4}{\int }}{x}^2\sqrt{x}dx$

d) $\underset{-1}{\overset{0}{\int }}{2}^{3x+2}dx$

e) $\underset{0}{\overset{2}{\int }}{2}^x{.3}^{x+1}dx$

g) $\underset{0}{\overset{1}{\int }}\frac{7^x}{{11}^x}dx$

Lời giải chi tiết

a) $\underset{-1}{\overset{1}{\int }}{(x+2)}^{3}dx={\frac{{(x+2)}^4}{4}|}_{-1}^1=20$

b) $\underset{1}{\overset{2}{\int }}\frac{2}{x^2}dx={-\frac{2}{x}|}_1^2=1$

c) $\underset{1}{\overset{4}{\int }}{x}^2\sqrt{x}dx=\underset{1}{\overset{4}{\int }}{x}^{\frac{5}{2}}dx={\frac{2}{7}{x}^{\frac{7}{2}}|}_1^4=\frac{254}{7}$

d) $\underset{-1}{\overset{0}{\int }}{2}^{3x+2}dx={\frac{2^{3x+2}}{3.\ln 2}|}_{-1}^0=\frac{4}{3\ln 2}-\frac{1}{6\ln 2}$

e) $\underset{0}{\overset{2}{\int }}{2}^x{.3}^{x+1}dx=\underset{0}{\overset{2}{\int }}{6}^x.3dx={\frac{{3.6}^x}{\ln 6}|}_0^2=\frac{105}{\ln 6}$

g) $\underset{0}{\overset{1}{\int }}\frac{7^x}{{11}^x}dx={\frac{{\left(\frac{7}{11}\right)}^x}{\ln \frac{7}{11}}|}_0^1=\frac{-4}{11\ln \frac{7}{11}}$