Math Integration MCQs

Differential of y can be identified as

(a) dy

(b) \frac{dy}{dx}

(c) dy ‘

(d) dx

Answer (a) dy

Select the Differential of x

(a) \frac{dx}{dy}

(b) 1

(c) dy

(d) dx

Answer (a) \frac{dx}{dy}

The Integration is the opposite procedure of

(a). tabulation

(b). differentiation

(c). classification

(d). sublimation
Answer (b). differentiation

Follwing is n \neq – 1 , \int x^{n} dx =

(a). \frac{x^{n+1}}{n+1} + c

(b). \frac{x^{n-1}}{n-1} + c

(c). \frac{x^{n+1}}{n} + c

(d). x^n + c
Answer (a). \frac{x^{n+1}}{n+1} + c

Select the correct one for the following \int \frac{d}{dx}x^n dx =

(a). \frac{x^{n+1}}{n} + c

(b). x^n + c

(c). \frac{x^{n+1}}{n+1} + c

(d). \frac{x^{n-1}}{n-1} + c

Answer (b). x^n + c

select correct for the t\int ln xdx =

(a). x – x ln x

(b). x ln x – x

(c). x log_a x + x

(d). \frac{1}{x} ln x

Answer (b). x ln x – x

Chooce correct one for the following \intsec5x tan5xdx =

(a). 5 sec5x+c

(b). \frac{1}{5} secx+c

(c. \frac{sec5x}{5}+c

(d). \frac{tan5x}{5}+c

Answer (c. \frac{sec5x}{5}+c

Select correct one for the following \int – sinxdx =

(a). cosx+c

(b). sinx

(c). -cosx+c

(d). – sinx +c

Answer (a). cosx+c

choose the correct one for the following \intcos2xdx=

(a). \frac{1}{2} sin2x +c

(b). 2 sin2x+c

(c). –\frac{1}{2} sin2x +c

(d). – 2sin2x+c

Answer (a). \frac{1}{2} sin2x +c

Select from the following If n\neq -1 , then \int [f(x)]^n f ‘(x) dx =

(a). \frac{[f(x)]^{n-1}}{n}+c

(b). \frac{[f(x)]^{n+1}}{n+1}+c

(c). \frac{[f(x)]^{n-1}}{n-1}+c

(d). n[f(x)]^{n-1}+c

Answer (b). \frac{[f(x)]^{n+1}}{n+1}+c
Select fro the following for \int x^{-1}dx

(a). lnx + c

(b). – x^{-2}

(c). \frac{x^{-2}}{0}

(d). 0

Answer (a). lnx + c

Select for the following \int cos(\frac{ln sinx}{sinx})dx=

(a). 1\2 (lnsinx)²+c

(b). 1\2 ln (sinx)²+c

(c). (lnsinx)²+c

(d). ln (sinx)²+c

Answer (a). 1\2 (lnsinx)²+c

Select correect for the \int e^{nx}dx=

(a). e^{nx+1}+c

(b). \frac{e^{nx}}{n}+c

(c). ln \: e^{nx}+c

(d). e^{nx}+c

Answer (b)\frac{e^{nx}}{n}+c

Choose for the following \int x e^{x}dx=

(a). x e^{x}-e^{x}+c

(b). e^{x}+x+c

(c). x e^{x}+e^{x}+c

(d). x e^{x}+c

Answer (a). x e^{x}-e^{x}+c

which is correct for the following \int \frac{1}{ax+b}dx =

(a). \frac{1}{a} ln ( ax + b ) +c

(b) . a ln ( ax + b ) +c

(c). ln ( ax + b ) +c

(d). log_a ( ax + b ) +c

Answer (a). \frac{1}{a} ln ( ax + b ) +
c
Select correect for \int \frac{e^{tan^{-1}x}}{1+x^2}dx=

(a). e^{secx}+c

(b). e^{tan^{-1}x}+c

(c). e^{cot^{-1}x}+c

(d). e^{tanx}+c

Answer (b). e^{tan^{-1}x}+c
which is correc for the following \int a^{x}dx=

(a). \frac{1}{a^x ln\; a}+c

(b). \frac{ln\; a}{a^{x}}+c

(c). \frac{a^{x}}{ln\; a}+c

(d). a^x \; ln \; a +c

Answer (c). \frac{a^{x}}{ln\; a}+c

which is correct for the following\int \frac{1}{1+x^2}dx=

(a). sin^{-1}x+c

(b). cot^{-1}x+c

(c). cos^{-1}x+c

(d). tan^{-1}x+c

Answer (d). tan^{-1}x+c
which is correc for the following\int (e^x+1)dx=

(a). e^{x}

(b). e^{x}+x^3+c

(c). e^{x}+x^2+c

(d). e^{x}+x+c

Answer (d). e^{x}+x+
Following is \int \frac{dx}{\sqrt{a^2-x^2}}=

(a). sin^{-1}(\frac{x}{a})+c

(b). cos^{-1}(\frac{x}{a})+c

(c). sin^{-1}(\frac{a}{x})+c

(d). sin^{-1}x+c

Answer (a). sin^{-1}(\frac{x}{a})+c

Prof. Fazal Rehman Shamil
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