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
