# Test: Integration I - Normal

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Question 1:   Find the antiderivative of the function $f\left(x\right)={x}^{2}+2x$
$F\left(x\right)=\frac{{x}^{3}}{3}+{x}^{2}+C$
$F\left(x\right)=\frac{{x}^{3}}{3}+2{x}^{2}+C$
$F\left(x\right)=\frac{{x}^{3}}{3}+\frac{{x}^{2}}{2}+C$
$F\left(x\right)=\frac{{x}^{3}}{3}+{x}^{2}$
Question 2:   Find the antiderivative of the function $f\left(x\right)=\mathrm{cos}\left(2x\right)+5$
$F\left(x\right)=\frac{\mathrm{sin}\left(2x\right)}{2}+5x$
$F\left(x\right)=\frac{\mathrm{sin}\left(2x\right)}{2}+5x+C$
$F\left(x\right)=\mathrm{sin}\left(2x\right)+5x+C$
$F\left(x\right)=\frac{\mathrm{sin}\left(2x\right)}{2}+C$
Question 3:   Find the antiderivative of the function $f\left(x\right)=7$
$F\left(x\right)=7x$
$F\left(x\right)=7x+C$
$F\left(x\right)=0$
$F\left(x\right)=C$
Question 4:   Find the antiderivative of the function $f\left(x\right)=\frac{1}{x}+4x$
$F\left(x\right)=\mathrm{ln}|x|+2{x}^{2}+C$
$F\left(x\right)=\mathrm{ln}|x|+2{x}^{2}$
$F\left(x\right)=\mathrm{ln}|x|+4{x}^{2}+C$
$F\left(x\right)=\mathrm{ln}|x|+{x}^{2}+C$
Question 5:   Find the antiderivative of the function $f\left(x\right)=\frac{2}{{\mathrm{sin}}^{2}\left(x\right)}-3{e}^{x}$
$F\left(x\right)=-2\mathrm{cot}\left(x\right)-3{e}^{x}$
$F\left(x\right)=-2\mathrm{tan}\left(x\right)-3{e}^{x}+C$
$F\left(x\right)=-2\mathrm{cot}\left(x\right)-3{e}^{x}+C$
$F\left(x\right)=\mathrm{cot}\left(x\right)-3{e}^{x}+C$
Question 6:   Calculate $\underset{0}{\overset{1}{\int }}\left({x}^{2}+2\right)dx$
$\frac{7}{3}$
$0$
$1$
$\frac{5}{3}$
Question 7:   Calculate $\underset{0}{\overset{\frac{\pi }{2}}{\int }}\left(\mathrm{cos}\left(x\right)-\mathrm{sin}\left(x\right)\right)dx$
$2$
$0$
$1$
$\frac{\pi }{2}$
Question 8:   Calculate $\underset{1}{\overset{2}{\int }}\left(3x-2\right)dx$
$25$
$20.5$
$1$
$20$
Question 9:   Calculate $\underset{0}{\overset{\pi }{\int }}\left(\frac{1}{{\mathrm{cos}}^{2}\left(x\right)}-\mathrm{sin}\left(x\right)\right)dx$
$1$
$0$
$2$
$-2$
Question 10:   Calculate $\underset{2}{\overset{4}{\int }}\left(4{x}^{3}-x\right)dx$
$256$
$200$
$240$
$234$