06.12 Integration and Accumulation of Change Exam Part One

Find the trapezoidal Riemann sum approximation of the integral from 1 to 5 of the square root of quantity x squared plus 3 close quantity times dx using four equal partitions.

(0.5)[f(1) + f(5)] + f(2) + f(3) + f(4)

Evaluate integral from 3 to 6 of the square root of x minus 2 dx by using substitution.

14/3

Which of the following is equivalent to the integral from negative 4 to negative 2 of negative 2x plus 2 dx question mark (10 points)

0.5(10 + 6) • 2

A piecewise function made up of a triangle, a rectangle, and a semicircle is shown. Piecewise graph made up of a triangle and a semicircle. The triangle begins at (-10, 0), increases to (-5, 10), and decreases to (5,0). The semicircle begins at (5,-5), decreases to (10,-10), and increases to (15,-5). Find the accumulation of change under the curve from x = −10 to x = 10 using geometric formulas.

30.365 units^2

the integral from 2 to t of quantity 2x times square root of x minus e to the power of x plus 1 close quantity over e dx equals ?

4 times the square root of t to the power of 5 all over 5e minus 16 root 2 over 5e minus e to the t plus e squared

Which of the following is an antiderivative of quantity of x squared plus 1 over x close quantity squared? I. one fifth x to the power of 5 plus x squared minus 1 over x II. one fifth x to the power of 5 plus x squared minus 1 over x minus 2 III. one fifth x to the power of 5 plus x squared plus ln absolute value of x squared close absolute value plus 3

I and II

A squirrel traveling along a straight telephone wire from its starting position at a speed of 65 inches per minute for 3 minutes is represented by the function s(t), where t is the number of minutes traveled. What units describe the area under the curve of s(t)?

Inches

Which integral can be approximated by a left Riemann sum where f(x) = 3x^2 − 2 on the interval [3, 7]? (10 points)

the integral from 3 to 7 of 3 times x squared minus 2 dx

What integral can be approximated with the following: the sum from i equal 1 to n of quantity 1 over 4 times parentheses negative 3 plus 5i over n close parentheses cubed close quantity times 5 over n?

the integral from negative 3 to 2 of 1 over 4 x cubed dx

If integral from negative 2 to 3 of the quantity 2 times f of x plus 2 end quantity dx equals 18 and integral from 1 to negative 2 of f of x dx equals negative 6 comma then integral from 1 to 3 of f of x dx is equal to which of the following?

−2