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11th Maths Monthly Test - 1 ( Integral Calculus )

St. Britto Hr. Sec. School - Madurai

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

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

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

\(\int {e^{6logx}-e^{5logx}\over e^{4logx}-e^{3logx}}dx\) is

x+c
\({x^3\over 3}+c\)
\({3\over x^3}+c\)
\({1\over x^2}+c\)

\(\int { \frac { 4\left( sin^{ -1 }x \right) ^{ 3 } }{ \sqrt { 1-{ x }^{ 2 } } } } \) dx = ________+c.

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

\(\int x^2e^{x\over2}dx\) is

\( x^2e^{x\over2}-4xe^{x\over2}-8e^{x\over2}+c\)
\( 2x^2e^{x\over2}-8xe^{x\over2}-16e^{x\over2}+c\)
\( 2x^2e^{x\over2}-8xe^{x\over2}+16e^{x\over2}+c\)
\( x^2{e^{x\over2}\over 2}-{xe^{x\over2}\over 4}+{e^{x\over2}\over 8}+c\)

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

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

\(\int sin \sqrt{xdx}\) is

\(2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c\)
\(2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c\)
\(2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c\)
\(2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c\)

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

\(\int {e^x(1+x)\over cos^2(xe^x)}dx\) is

cot(xe^x)+c
sec(xe^x)+c
tan(xe^x)+c
cos(xe^x)+c

If\(\int f'(x)e^{x^2}dx=(x-1)e^{x^2}+c\),then f(x) is

\(2x^3-{x^2\over 2}+x+c\)
\({x^3\over 2}+3x^2+4x+c\)
x³+4x²+6x+c
\({2x^3\over3}-x^3+x+c\)

\(\int {sec^2x\over tan^2 \ x-1}\) dx

\(2log|{1-tan x\over 1+tan \ x}|+c\)
\(log|{1+tan x\over 1-tan \ x}|+c\)
\({1\over2}log|{tan x+1\over tan \ x-1}|+c\)
\({1\over2}log|{tan x-1\over tan \ x+1}|+c\)

Part - B

Generic 2 - Answer All Question

Integrate the following with respect to x: sin(2x+ 4)

Find the integrals of the following : \({1\over 4-x^2}\)

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

Integrate the following with respect to x:cos³ x.
Integrate the following with respect to x :\({2x-3\over x^2+4x-12}\)

Integrate the following with respect to x: \({1\over e^{-x}}\)

Integrate the function with respect to x
\(\sqrt { { \left( x+1 \right) }^{ 2 }+4 } \)

Integrate the following with respect to x:\(4cos(5-2x)+9e^{3x-6}+{24\over 6-4x}\)

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

Given f"(X) = 6x + 6f(0) = -5 and f(1) = 6 find f(x)

Part - C

Generic 3 - Answer All Question

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

Evaluate \(\int { \frac { { sin }^{ 6 }x+cos^{ 6 }x }{ sin^{ 2 }xcos^{ 2 }x } } \)

Evaluate :\(\int {3x+7\over x^2-3x+2}dx\)

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

Integrate the following with respect to x.\(x^2e^{5x}\)
Integrate the following with respect to x\({sin\sqrt{x}\over \sqrt{x}}\)

Integrate the following functions with respect to x: sin² 5x

Integrate the following with respect to x :\({2x+1\over \sqrt{9+4x-x^2}}\)

Evaluate the following :\(\int \sqrt{(x-3)(5-x)}dx\)

Evaluate the following integrals: \({12\over (4x-5)^3}+{6\over 3x+2}+16e^{4x+3}\)

Part - D

Generic 5 - Answer All Question

Integrate the following functions with respect to x :\((3x+4)\sqrt{3x+7}\)

Evaluate sec³2x

Evaluate the following integrals\(\int {x^2\over x^2+5}dx\)

Integrate the following with respect to x\(tan \ x\sqrt{sec \ x}\)

Integrate the following with respect to x\({1\over xlog \ xlog(log \ x)}\)

Integrate the following with respect to x : \(e^{-3x}cos \ x\)
Evaluate the integral
\(\cfrac { 6x+7 }{ \sqrt { (x-4)(x-5) } } \)

The rate of change of weight of person w in kg with respect to their height h in centimetres is given approximately by \({dw\over dh}=4.364 \times 10^{-5}h^2\). Find weight as a function of height. Also find the weight of a person whose height is 150 cm.

Integrate the following functions with respect to x: cosec(5x+3)cot(5x+3)

Find the integrals of the following : \({1\over \sqrt{(2+x)^2-1}}\)

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