DAE MATH-223

Applied Mathematics-II

Chapter 9 : Definite Integrals and Applications

DAE Common Technologies | Second Year

Multiple Choice Questions

Chapter:09 (Definite Integrals and Applications)

Question 1:

\(\int_{0}^{1} \,dx =\)

-1 0 1 2

Question 2:

\(\int_{0}^{π/4}\, {{sec}^2}x \,dx =\)

1 2 Zero 3

Question 3:

If lower and upper limits of \(\int_{a}^{b}\,f(x)\,dx\) are replaced by each other then we get

\(\int_{a}^{b}\, f(x) \,dx\) \(-\int_{b}^{a}\, f(x) \,dx\) \(\pm\;\int_{a}^{b}\, f(x) \,dx\) \(\int_{b}^{a}\, f(x) \,dx\)

Question 4:

\(\int_{2}^{3}\, \frac{2x\;dx}{{x^2}+1} \)

\(\ln{2}\) \(\ln{10}-\ln{6}\) \(\ln{({x^2}+1)}\) \(\ln{10}+\ln{6}\)

Question 5:

\(\int_{1}^{3}\,{e^{2x}}\,dx\)

\({e^6}-{e^2}\) \({\frac{1}{2}}{({e^6}-{e^2})}\) \(\frac{e^{2x}}{2}\) \({\frac{1}{2}}{({e^6}+{e^2})}\)

Question 6:

\(\int_{1}^{2}\,{3{x^2}}\,dx =\)

7 8 6 9

Question 7:

\(\int_{0}^{1}\, {\frac{1}{{x^2}+1}} \,dx =\)

\(\frac{π}{4}\) \(0\) \(1\) \(-\frac{π}{4}\)

Question 8:

\(\int_{0}^{1}\,{\frac{1}{x{\sqrt{{x^2}-1}}}}\,dx =\)

\(-1\) \(1\) \(0\) \(-\frac{π}{2}\)

Question 9:

\(\int_{\frac{π}{3}}^{\frac{π}{2}}\,{\frac{{{cosec}^2}x}{cot x}}\,dx =\)

\(2\) \(\sqrt{3}\) \(\frac{1}{\sqrt{3}}\) \(\ln{\frac{1}{\sqrt{3}}}\)

Question 10:

\(\int_{0}^{\frac{π}{2}}\,{cot x}\,dx =\)

\(-1\) \(1\) \(0\) \(\frac{π}{2}\)

NOTE
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INSTRUCTOR
MUHAMMAD BIN JAMEEL
BSC ENGG. CIVIL

PBTE | DAE | MATH-223 APPLIED MATHEMATICS-I | MCQs | Chapter : 09 Definite Integrals and Applications