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Engineering Math Practice Test: Integral Calculus
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Avg score: 70% • Most missed: “Integration of (Sin(x) – Cos(x))ex is ___________”

Integral Calculus topics include: integral reduction formula, improper integrals, quadrature, rectification, surface area and volume of solid, polar and parametric forms rectification.
 

Engineering Math Practice Test: Integral Calculus
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25 Questions

1. Find the area ln(x)⁄x from x = x = aeb to a.
2. Rectification is determining ____________
3. Temperature of a rod is increased by moving x distance from origin and is given by equation T(x) = x2 + 2x, where x is the distance and T(x) is change of temperature w.r.t distance. If, at x = 0, temperature is 40 C, find temperature at x=10.
4. Find the length of the curve given by the equation.
\(x^{\frac{2}{3}}+y^\frac{2}{3}=a^\frac{2}{3}\)
5. Find \(\int_{0}^{\frac{\pi}{2}} sin^6(x)dx\).
6. Find \(\int_{-\infty}^{0}x^5.e^x dx\).
7. The volume of solid of revolution when rotated along x-axis is given as _____________
8. Value of ∫uv dx,where u and v are function of x.
9. Find the value of \(\int \frac{sec^4⁡(x)}{\sqrt{tan⁡(x)}} dx\).
10. Find \(\int_{0}^{\frac{\pi}{4}} tan^3(x)dx\).
11. Find the value of \(\int \frac{1}{4x^2+4x+5} dx\).
12. If differentiation of any function is infinite at any point and constant at other points then it means ___________
13. Find the value of ∫tan-1⁡(x)dx.
14. Find the value of ∫ cot3(x) cosec4 (x).
15. The expression for arc length in rectangular form is_________________
16. If differentiation of any function is zero at any point and constant at other points then it means?
17. The arc length of y = cosh⁡x where x varies from 0 to 1 is ____________
18. Find \(\int_{0}^{\frac{\pi}{2}} cos^3(x).cos(2x)dx\).
19. Closed form solutions are absent for ellipses.
20. Find \(\int_{0}^{\frac{\pi}{4}} x^4.sin(x)dx\).
21. Find \(\int_{0}^{\frac{\pi}{2}} sin^{10}(x)cos(x)dx\).
22. Find \(\int_1^{\sqrt{2}} (x^{\frac{8}{5}}-\frac{1}{x^{\frac{2}{5}}})^{\frac{5}{2}}dx\).
23. Which one of the following is an infinite curve?
24. The volume of solid of revolution when rotated along y-axis is given as ________
25. Find the value of \(\int_{0}^{\frac{\pi}{2}} cos^{11}(x).sin^9(x)\, dx\).

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