Unit 6A Review - AP Calculus

 $\frac{\text{d}}{\text{d}x}\int_2^x\ln t\ dt=$  

•  $\ln x$  

•  $\ln2$  

•  $\frac{1}{x}$  

•  $\frac{1}{2}$  

•  $\ln x\ -\ \ln2$  

If $g\left(x\right)=\int_{\pi}^{\pi x}\cos\left(t^2\right)dt$  then  $g'\left(x\right)=$  

•  $\sin\left(\pi^2x^2\right)$  

•  $\pi x\sin\left(\pi^2x^2\right)$  

•  $\pi x\cos\left(\pi^2x\right)$  

•  $\pi\cos\left(\pi^2x^2\right)$  

  $\frac{\text{d}}{\text{d}x}\int_{\sin x}^4\sqrt{1+t^2}\ dt\ =$  

•  $\sqrt{1+\sin^2x}$  

•  $-\cos x\sqrt{1+\sin^2x}$  

•  $-\sqrt{1+\sin^2x}$  

•  $\cos x\sqrt{1+\sin^2x}$  

If f has two continuous derivatives on [5, 10] , then

 $\int_5^{10}f''\left(t\right)dt\ =\$  

•  $f''\left(10\right)\ -\ f''\left(5\right)$  

•  $f'\left(10\right)\ -\ f'\left(5\right)$  

•  $f\left(10\right)\ -\ f\left(5\right)$  

•  $\frac{1}{5}\left(f'\left(10\right)\ -\ f'\left(5\right)\right)$  

The graph of  $g'\left(x\right)$  is given below, if g(3) = 6  find g(0).

• 1

• 2

• 4

• 6

The graph of f is given below.   $F\left(x\right)=\int_0^x\ f\left(t\right)dt$   Which of the statements below is true?

• F is decreasing on (1,2)

• F has a relative minimum at x = 2

• F is decreasing on (2, 4)

• F has a relative maximum at x = 1.

• F has a point of inflection at x = 4.

If

 $f\left(x\right)=\int_{-2}^xf'\left(t\right)dt\$  where  $f'\left(t\right)$    is shown in the figure below, find the equation of the tangent line to f at  $x=3$  

• y=18

• y = 2x + 18

• y = 2x + 12

• y = 2x + 2

The function f(x) is continuous on the inteval [-5, 11], and selected values are given below. The trapezoidal approximation for  $\int_{-5}^6f\left(x\right)dx$  found with 4 subintervals, is zero.  Find k.

• -9/10

• -2/3

• -21/31

• -16/19

 $\int_0^{\pi}\cos x\ dx$  

Which of the limits is equivalent to the following definite integral?

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\cos\left(\frac{\pi i}{n}\right)\cdot\frac{\pi}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\cos\left(\frac{\pi i}{n}\right)\cdot\frac{i}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\cos\left(\frac{i}{n}\right)\cdot\frac{i}{n}$  

•  $\lim_{n\rightarrow\infty}\sum_{i=1}^n\cos\left(\frac{i}{n}\right)\cdot\frac{\pi}{n}$  

Given  $g'\left(x\right)=\ln\left(x+7\right)$  and  $g\left(2\right)\ =\ 6$  determine the value of  $g\left(3\right)$  .

• -3.749

• 1.648

• 7.321

• 8.250