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Syllabus

/(x^{2}-1)^{3/2}dx^{x}(1+x)/cos^{2}(xe^{x}) dx is equal toB denotes the value of the product of

mandn, if ${2}^{m}=3and{3}^{n}=4.$,C denotes the sum of the integral roots of the equation ${\mathrm{log}}_{3x}\left(\frac{3}{x}\right)+{\left({\mathrm{log}}_{3}x\right)}^{2}=1.$

The value of A + B equals

(A) 10 (B) 6 (C) 8 (D) 4

The value of B + C equals

(A) 6 (B) 2 (C) 4 (D) 8

The value of A + C$\xf7$B equals

(A) 5 (B) 8 (C) 7 (D) 4

pi/4; pi/2; 1; 1000.

(pls. tell wch formula to be applied..)

1. Integral 0 to pi/2( sin

^{2}xdx/sinx+cosx)2.Integral 0 to pi/2 (sin

^{2}xdx/(1+sinxcosx))In a shorter method

tan x tan 2x tan 3x dx

1.

Integarl 0 to pi ((xtanx)dx/(secx+tanx))2. Integral 0 to pi/2 ((xsinxcosx)dx/(sin

^{4}x+cos^{4}x)(cos 4x + 1)/(cos x-tan x)dx

-x/y; y/x; -y/x; x/y.

cos(2x)/[(sinx+ cosx)

^{2}]Answer with explanation.

SOLVE QUESTION NO. 67 AND 77. (NOTE: SOLVE BOTH THE QUESTIONS AND DO NOT GIVE ANY LINKS)

$\int {\mathrm{sin}}^{-1}xdx.$

^{1/2}cot(x) / {(sinx)

^{1/2}}Solve this. $\int {\text{sin}}^{2}{\text{xcos}}^{4}\text{xdx}$

$\Rightarrow {\int}_{-1}^{1}\frac{x}{\sqrt{1-{x}^{2}}},{\mathrm{sin}}^{-1}\left(2x\sqrt{1-{x}^{2}}\right).dx$

Question 75 of 90

The value of ${\int}_{-\mathrm{\pi}/2}^{\mathrm{\pi}/2}\left(p{\mathrm{sin}}^{3}x+q{\mathrm{sin}}^{4}x+r{\mathrm{sin}}^{5}x\right)dx$ depends on :

1. p

2. q

3. r

4. p and q

Question 76 of 90

${\int}_{0}^{\mathrm{\pi}/2}\frac{dx}{1+{\mathrm{tan}}^{3}x}$ is :

1. 0

2. 1

3. $\mathrm{\pi}$/2

4. $\mathrm{\pi}$/4

Question 63 of 90

The value of ${\int}_{0}^{\mathrm{\pi}/2}\frac{\sqrt{\mathrm{sin}x}}{\sqrt{\mathrm{sin}x}+\sqrt{\mathrm{cos}x}}dx$ is

1. p/2

2. p/3

3. $\mathrm{\pi}$/4

4. p

^{5}x+Cos^{5}x)$Question70of90\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\underset{0}{\overset{x}{\int}}\left[\mathrm{sin}t\right]dtwhereintegerx\in (2n\mathrm{\pi},\left(4\mathrm{n}+1\right)\mathrm{\pi},\mathrm{n}\in \mathrm{N}\mathrm{and}\left[.\right]denotesthegreatestintegerfunctionisequalto.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{1}\mathbf{.}-n\mathrm{\pi}\phantom{\rule{0ex}{0ex}}\mathbf{2}\mathbf{.}\mathbf{}-\left(\mathrm{n}+1\right)\mathrm{\pi}\phantom{\rule{0ex}{0ex}}\mathbf{3}\mathbf{.}-2\mathrm{n\pi}\phantom{\rule{0ex}{0ex}}\mathbf{4}\mathbf{.}-2\left(\mathrm{n}+1\right)\mathrm{\pi}$

Question 85 of 90

If $I={\int}_{-1}^{1}\left(\frac{{x}^{2}+\mathrm{sin}x}{1+{x}^{2}}\right)dx$ then

1. 0

2. 2

3. pi/2

4. 2-pi/2

Q: ∫a

^{3x+3}x is equal toQ. Evaluate : $\int \frac{\mathrm{tan}\left(\mathcal{l}\mathrm{n}\left(\mathrm{x}+\sqrt{1+{\mathrm{x}}^{2}}\right)\right)}{\sqrt{1+{\mathrm{x}}^{2}}}\mathrm{dx}$.

Q: ∫(e

^{1/x}+1)/x^{2}dx is equal toQuestion 62 of 90

${\int}_{-2}^{2}min\left(x-\left[x\right],-x-\left[-x\right]\right)dx$, where [.] is the greatest integer function =

1. 0

2. 1

3. 2

4. None of these.

$\mathbf{Q}\mathbf{.}\mathbf{}\mathrm{If}\mathrm{f}\left(\mathrm{a}+\mathrm{b}-\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)\mathrm{then}\underset{\mathrm{a}}{\overset{\mathrm{b}}{\int}}\mathrm{x}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\mathrm{is}\mathrm{equal}\mathrm{to}\phantom{\rule{0ex}{0ex}}1.\frac{\mathrm{a}-\mathrm{b}}{2}\underset{\mathrm{a}}{\overset{\mathrm{b}}{\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\phantom{\rule{0ex}{0ex}}2.\left(\frac{\mathrm{a}+\mathrm{b}}{2}\right)\underset{\mathrm{a}}{\overset{\mathrm{b}}{\int}}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\phantom{\rule{0ex}{0ex}}3.0\phantom{\rule{0ex}{0ex}}4.\mathrm{none}\mathrm{of}\mathrm{these}$