TEST 34
1.
\(\displaystyle\int\limits_{-3}^{3} (x^2+3)\,dx=?\)
A) \(40\)B) \(36\)C) \(32\)D) \(24\)E) \(18\)
2.
\(\samefrac{\displaystyle\int\limits_{-5}^{5} (\cos^2x+x^4+|x|)\,dx}{\displaystyle\int\limits_{0}^{5} (\cos^2x+x^4+|-x|)\,dx}=?\)
A) \(2\)B) \(1\)C) \(\samefrac{1}{2}\)D) \(-1\)E) \(-2\)
3.
\(f(x)=\displaystyle\int\limits_{1}^{2x} (x^2+x+1)\,dx\)
\(\Rightarrow f'(1)=?\)
A) \(14\)B) \(12\)C) \(10\)D) \(8\)E) \(6\)
4.
\(\displaystyle\int\limits_{-3}^{3} \sqrt{9-x^2}\,dx=?\)
A) \(9\pi\)B) \(6\pi\)C) \(\samefrac{11\pi}2\)D) \(\samefrac{9\pi}2\)E) \(3\pi\)
5.
\(\Rightarrow \displaystyle\int\limits_{-3}^{3} (\left[\!\left[ f(x)\right]\!\right])\,dx=?\)
A) \(6\)B) \(3\)C) \(0\)D) \(-2\)E) \(-3\)
6.
\(\Rightarrow\text{Shaded Area}=?\)
A) \(\displaystyle\int\limits_{1}^{2} \sqrt{4-y^2}\,dy\)B) \(\displaystyle\int\limits_{0}^{1} \sqrt{2-x^2}\,dx\)C) \(\displaystyle\int\limits_{0}^{2} \sqrt{4-y}\,dy\)D) \(\displaystyle\int\limits_{1}^{2} \sqrt{4-x^2}\,dx\)E) \(\displaystyle\int\limits_{1}^{2} \sqrt{2-x^2}\,dx\)
7.
\(\Rightarrow\text{Shaded Area}=?\)
A) \(\samefrac1{\sqrt2}\)B) \(\samefrac{3+\sqrt2}2\)C) \(\samefrac{1-\sqrt2}2\)D) \(\samefrac{9}{2}\)E) \(\samefrac{1+4\sqrt2}2\)