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11th Maths Weekly Test - 1 ( Integral Calculus )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 1 ( Integral Calculus )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

\(\int{ {e^x}(x^2 \ tan^{-1}x+tan^{-1}x+1)\over x^2+1}dx\) is

e^xtan^-1(x+1)+c
tan^-1(e^x)+c
\(e^x{(tan^{-1}x)^2\over 2}+c\)
e^x tan^-1 x+c

\(\int {x+2\over \sqrt{x^2-1}}dx\)is

\(\sqrt{x^2-1}-2 log|x+\sqrt{x^2-1}|+c\)
\(sin^{-1}x-2 log|x+\sqrt{x^2-1}|+c\)
\(2 log|x+\sqrt{x^2-1}|-sin^{-1}x+c\)
\(\sqrt{x^2-1}+2log|x+\sqrt{x^2-1}|+c\)

\(\int { \left| x \right| ^{ 3 } } \) dx is equal to ________+c.

\(\frac { -{ x }^{ 4 } }{ 4 } +c\)
\(\frac { \left| x \right| ^{ 4 } }{ 4 } \)
\(\frac { { x }^{ 4 } }{ 4 } \)
none of these

\(\int tan^{-1}\sqrt{1-cos \ 2x\over 1+cos \ 2x}dx\) is

x²+c
2x²+c
\({x^2\over2}+c\)
\(-{x^2\over2}+c\)

\(\int { \frac { \left( 1+logx \right) ^{ 2 } }{ x } } \) dx = _______+C.

\(\frac { \left( 1+logx \right) ^{ 3 } }{ 3 } \)
3 log ( 1 + log x)
2(1 + log x)
none of these

\(\int { \frac { 1 }{ 2 } } { sec }^{ 2 }\) x dx is _____ + c.

\(\frac { 1 }{ 2 } \) tan x
tan x
2 tan x
none of these

\(\int { \frac { \left( log{ x } \right) ^{ 3 } }{ x } } \) dx = _________+c.

\(\frac { \left( log{ x } \right) ^{ 4 } }{ 4 } \)
(sin^-1 x)⁴
(log x)⁴
\(\frac { 1 }{ 3logx } \)

\(\int{x^2+cos^2x\over x^2+1}cosec^2xdx\) is

cot x+sin ^-1x+c
-cot x+tan^-1x+c
-tan x+cot^-1x+c
-cot x-tan^-1x+c

The gradient (slope) of a curve at any point (x, y) is\({x^2-4\over x^2}\). If the curve passes through the point (2, 7), then the equation of the curve is

\(y=x+{4\over x}+3\)
\(y=x+{4\over x}+4\)
y=x²+3x+4
y=x²-3x+6

If \(\int {3^{1\over x}\over x^2}dx=k(3^{1\over x})+c\) ,then the value of k is

log 3
-log 3
\(-{1\over log3}\)
\({1\over log3}\)

Part - B

Generic 2 - Answer All Question

Integrate the following functions with respect to x:\((x+5)^6\)

Integrate the function with respect to x
\(\cfrac { \sqrt { tanx } }{ sinxcosx } \)

Solve \(\cfrac { 1 }{ { sin }^{ 2 }(1-mx) } \)

Integrate the following with respect to x e^2xsin x

Part - C

Generic 3 - Answer All Question

Integrate the function with respect to x
\(\sqrt { { x }^{ 2 }-3x+10 } \)

Evaluate : \(\int {(x-1)^2\over x^3+x}dx\)

Evaluate the following :\(\int \sqrt{(x-3)(5-x)}dx\)
Integrate the following with respect to x\({10x^9+10^xlog_e10\over 10^x+x^{10}}\)

Evaluate the following :\(\int \sqrt{x^2+x+1}dx\)

Part - D

Generic 5 - Answer All Question

Integrate the following functions with respect to x:\(sec^2{x\over5}\)

Evaluate the integral
\(\cfrac { 2x-3 }{ \sqrt { 10-7x-{ x }^{ 2 } } } \)

Integrate the following with respect to x :\({2x+3\over \sqrt{x^2+4x+1}}\)
Integrate the following functions with respect to x :\({1\over \sqrt{x+3}-\sqrt{x-4}}\)

Integrate the following with respect to x:\({log \ x \over (1+log x)^2}\)

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