Applications: Area Between Curves — Engineering Board Exam Practice Questions

16 free engineering board exam reviewer questions on Applications: Area Between Curves (Integral Calculus), each with the correct answer and a worked solution.

1. Find the area bounded by y=x2 and y=4.
2. Find the area under the curve y=x3 from x=0 to x=2.
3. Find the area enclosed between y=x and y=x2 from x=0 to x=1.
4. Find the area between the curve y=6x-x2 and the x-axis.
5. Find the area bounded by y=sqrt(x), the x-axis, and x=4.
6. Find the area between y=x2 and y=2x from x=0 to x=2.
7. Find the area enclosed by the astroid x=2 3t, y=2 3t.
8. Find the total area enclosed by the lemniscate r2=16 2 .
9. Find the area of the region that lies inside the circle r=3 and outside the cardioid r=1+ .
10. Find the area of one petal of the rose r=4 3 .
11. Find the area enclosed by the cardioid r=2(1+ ).
12. Find the area bounded by y= x and y= x between x= π4 and x=5π/4.
13. Find the area of the region bounded by the parabola y2=4x and the line y=2x-4.
14. Find the area bounded by y=ex, y=e-x, and the line x= 3.
15. Find the area under one arch of the cycloid x=3(t- t), y=3(1- t).
16. Find the area of the region bounded by the parabolas y=x2 and y=8-x2.