PBTE | DAE | MATH-212 APPLIED MATHEMATICS-I | MCQs | Chapter : 06 Methods of Integration

DAE MATH-212

Applied Mathematics-II

Chapter 6 : Methods of Integration

DAE Common Technologies | Second Year

Multiple Choice Questions

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Chapter:06 (Methods of Integration)

Question 1:

\(\int{\frac{1}{\sqrt{1-{x^2}}}}dx=\)

\({{Sin}^{-1}}x\) \({{Cos}^{-1}}x\) \({{Sec}^{-1}}x\) \({{tan}^{-1}}x\)

Question 2:

\(\int{\frac{-1}{\sqrt{1-{x^2}}}}dx=\)

\({{Sin}^{-1}}x\) \({{Cos}^{-1}}x\) \({{Sec}^{-1}}x\) \({\sqrt{1-{x^2}}}\)

Question 3:

\(\int{\frac{e^x}{1+{e^x}}}dx=\)

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

Question 4:

\(\int{\frac{Sec x tan x}{3 + Sec x}}dx=\)

\(Sec x + tan x\) \(3 + sec x\) \(\ln(3 + sec x)\) \(\ln(sec x + tan x)\)

Question 5:

\(\int{x sin x}dx=\)

\({- x Cos x + Sin x}\) \(Sin x\) \({x + Sin x}\) \({\frac{x^2}{2}}{cos x}\)

Question 6:

\(\int{{{Sin}^4}x}{Cos x}dx=\)

\(\frac{{{Sin}^5}x}{5}\) \(\frac{{{Sin}^5}x Cos x}{5}\) \(\frac{{{Cos}^2}x}{2}\) \({- sin x cos x}\)

Question 7:

\(\int{x {{Sec}^2}x}dx=\)

\(x tan x\) \(x tan x + \ln{sec}x\) \(Tan x\) \(x tan x - \ln sec x\)

Question 8:

\(\int{x{e^x}}=\)

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

Question 9:

\(\int{(ax+b)^3}dx=\)

\(\frac{(ax+b)^4}{4a}\) \(3{(ax+b)^2}\) \(\frac{(ax+b)^3}{4a}\) \(3 a {(ax+b)^2}\)

Question 10:

\(\int{Cosec{x}}dx=\)

\(\ln{(Cosec x - Cot x)}\) \(\ln{sec x}\) \(\ln{(Cosec x + cot x)}\) \(cos x\)

Quiz Results

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Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9

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INSTRUCTOR

MUHAMMAD BIN JAMEEL

BSC ENGG. CIVIL