MATH 180 Grossmont Cuyamaca Community Basic Calculus Exam please solve this exam and make it clear with good hand writing. show all steps. EXAM #4 Math 180

MATH 180 Grossmont Cuyamaca Community Basic Calculus Exam please solve this exam and make it clear with good hand writing. show all steps. EXAM #4 Math 180, Cuyamaca College
Instructor Alyssa Krauss, Spring 2020
Name_______________________________________________
1. Approximate the area under the curve y = sin(x) from 0 to

using 8 approximating rectangles of
equal widths and right endpoints. Round your answer to the nearest hundredth.
5
2
2. Evaluate the integral by interpreting it in terms of areas. ∫−5
√25 − 2 dx.
3. An animal population is increasing at a rate of 13 + 51t per year (where t is measured in years).
By how much does the animal population increase between the fourth and tenth years?
HINT: what does the word rate imply?
4. The velocity function (in meters per second) is given for a particle moving along a line. Find the
distance traveled by the particle during the given time interval. ( ) = 8 − 8
0≤ ≤5
9
5. Evaluate the integral: ∫0 (6 + 6 − 2 ) ⅆ
6. The area of the region that lies to the right of the y-axis and to the left of the parabola x = 2y – y2
2
(the shaded region in the figure) is given by the integral ∫0 (2 − 2 ) ⅆ .
Find the area.
7. Evaluate the indefinite integral: ∫ 9 ⅆ
8. Evaluate the indefinite integral: ∫
2 7 −5 4 +2
7
ⅆ

9. Evaluate the definite integral :∫06 (8 ) ⅆ Round your answer to 3 decimal places.
10. Sketch the region bounded by the graphs of the given equations and find the area of that region.
y = -x2 + 4, y = 2x + 1

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