TEST 39
1.
\(\displaystyle\int\samefrac{dx}{x\cdot\ln x}=?\)
A) \(\ln|x|+c\)B) \(\ln|\ln x|+c\)C) \(\ln|x+\ln|x||+c\)D) \(\samefrac x{\ln|x|}+c\)E) \(x-\ln|x|+c\)
2.
\(\displaystyle\int (x\cdot\sin x)\,dx=?\)
A) \(x\cdot\cos x-\sin x+c\)B) \(x\cdot\cos x+c\)C) \(\sin x-x\cdot\cos x+c\)D) \(\cos x-\sin x+c\)E) \(\sin^2x+c\)
3.
\(\displaystyle\int (\cos^3x\cdot\sin x)\,dx=?\)
A) \(-\samefrac{1}{4}\cos^4x+c\)B) \(\samefrac{1}{3}\cos^3x+c\)C) \(-\samefrac{1}{3}\cos^3x+c\)D) \(-\samefrac{1}{5}\cos^5x+c\)E) \(\samefrac{1}{5}\cos^5x+c\)
4.
\(\displaystyle\int\limits_{0}^{2} (x^2\cdot e^x)\,dx=?\)
A) \(2e^2-2\)B) \(2e^2\)C) \(4e^2\)D) \(8e^2-1\)E) \(16e^2\)
5.
\(\samefrac d{dx}\left(\displaystyle\int\limits_{-2}^{6} (x^2-7x)\,dx\right)=?\)
A) \(-11\)B) \(-7\)C) \(0\)D) \(7\)E) \(11\)
6.
\(\displaystyle\int x^2\cos x\,dx=?\)
A) \(x^2\cdot\sin x+x\cdot\cos x-\sin x+c\)B) \(x^2\cdot\sin x+x\cdot\cos x+\sin x+c\)C) \(x^2\cdot\sin x+2x\cdot\cos x-2\cdot\sin x+c\)D) \(x^2\cdot\sin x+2x\cdot\cos x+2\cdot\sin x+c\)E) \(x^2\cdot\sin x+4x\cdot\cos x-2\cdot\sin x+c\)
7.
\(\displaystyle\int (2x+f(x))\,dx=x^3+2x^2-4x+10\)
\(\Rightarrow f(x)=?\)
A) \(3x^2+4x\)B) \(3x^2+2x-4\)C) \(x^3+2x^2-2x-4\)D) \(3x^2+x\)E) \(3x^2-x\)
8.
\(\displaystyle\int\limits_{-2}^{2} \sqrt{4-x^2}\,dx=?\)
A) \(\pi\)B) \(2\pi\)C) \(4\pi\)D) \(6\pi\)E) \(8\pi\)