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IntegrationQuestion and Answers: Page 326

Question Number 20309 Answers: 0 Comments: 0

∫x^x dx

$\int x^{x} d x$

Question Number 20293 Answers: 1 Comments: 0

∫(√(((a+x)/x)dx))

$\int \sqrt{\frac{a + x}{x} d x}$

Question Number 20292 Answers: 1 Comments: 0

∫(dx/((x+1)^(1/2) +(√(x−1))))

$\int \frac{d x}{{(x + 1)}^{\frac{1}{2}} + \sqrt{x - 1}}$

Question Number 20291 Answers: 1 Comments: 0

(√(((1−x)/(1+x)) dx))

$\sqrt{\frac{1 - x}{1 + x} d x}$

Question Number 20449 Answers: 0 Comments: 0

∫(dx/(sin^(1/2) xcos^(7/2) x))

$\int \frac{d x}{\sin^{\frac{1}{2}} x \cos^{\frac{7}{2}} x}$

Question Number 20257 Answers: 1 Comments: 0

∫(dx/((1−x)(√(1+x))))

$\int \frac{d x}{(1 - x) \sqrt{1 + x}}$

Question Number 20256 Answers: 1 Comments: 0

∫(dx/((x−4)(√(x+3))))

$\int \frac{d x}{(x - 4) \sqrt{x + 3}}$

Question Number 20255 Answers: 1 Comments: 0

∫((x^3 dx)/(√(x−1)))

$\int \frac{x^{3} d x}{\sqrt{x - 1}}$

Question Number 20254 Answers: 1 Comments: 0

∫(dx/((x−1)(√(x^2 +1))))

$\int \frac{d x}{(x - 1) \sqrt{x^{2} + 1}}$

Question Number 20281 Answers: 0 Comments: 0

Compute the volume bounded by the surfaces: y=x^2 , x=y^2 , z=0, z=12+y−x^2 . [ Ans. ((549)/(144))]

$C o m p u t e t h e v o l u m e b o u n d e d b y$ $t h e s u r f a c e s : y = x^{2}, x = y^{2}, z = 0,$ $z = 12 + y - x^{2} .$ $[A n s . \frac{549}{144}]$

Question Number 20244 Answers: 1 Comments: 0

∫(dx/((2−x)(√x)))

$\int \frac{d x}{(2 - x) \sqrt{x}}$

Question Number 20243 Answers: 1 Comments: 0

∫(dx/(x+(√x)))

$\int \frac{d x}{x + \sqrt{x}}$

Question Number 20242 Answers: 1 Comments: 0

∫((5x^2 +11x+26)/(x^2 +2x+5))dx integration by partial fraction

$\int \frac{5 x^{2} + 11 x + 26}{x^{2} + 2 x + 5} d x$ $i n t e g r a t i o n b y p a r t i a l f r a c t i o n$

Question Number 20241 Answers: 1 Comments: 0

partial fraction ∫((2x^2 +5x−9)/(√(x^2 −x+1)))dx

$p a r t i a l f r a c t i o n$ $\int \frac{2 x^{2} + 5 x - 9}{\sqrt{x^{2} - x + 1}} d x$

Question Number 20239 Answers: 1 Comments: 0

∫(((2x+3)dx)/(√(x^2 +4x−7)))

$\int \frac{(2 x + 3) d x}{\sqrt{x^{2} + 4 x - 7}}$

Question Number 20238 Answers: 1 Comments: 1

∫(dx/(x^2 −x+1))

$\int \frac{d x}{x^{2} - x + 1}$

Question Number 20237 Answers: 0 Comments: 1

∫(e^(tan^(−1) x) /(1+x^2 ))dx

$\int \frac{e^{\tan^{- 1} x}}{1 + x^{2}} d x$

Question Number 20230 Answers: 1 Comments: 5

Question Number 20202 Answers: 0 Comments: 10

Is definite integral can have negative value? Because I think ∫_a ^b f(x) dx is total area below graph f(x) from x = a until x = b, so it can′t be negative

$Is definite integral can have negative value ?$ $Because I think \int_{a}^{b} f (x) d x is total area below$ $graph f (x) from x = a until x = b, so it {can}^{'} t$ $be negative$

Question Number 20167 Answers: 1 Comments: 0

please solve it integrate with respect to x ∫((5x−2)/(3x^2 +2x+1))

$p l e a s e s o l v e i t$ $i n t e g r a t e w i t h r e s p e c t t o x$ $\int \frac{5 x - 2}{3 x^{2} + 2 x + 1}$

Question Number 20166 Answers: 1 Comments: 0

∫cosec^2 xdx

$\int cosec^{2} x d x$

Question Number 20164 Answers: 1 Comments: 0

∫(e^(tan^(−1) x) /(1+x^2 ))

$\int \frac{e^{\tan^{- 1} x}}{1 + x^{2}}$

Question Number 20157 Answers: 1 Comments: 1

Question Number 20162 Answers: 1 Comments: 0

Compute the volume of a solid bounded by a surface with equation (x^2 +y^2 +z^2 )^2 =a^3 x .

$C o m p u t e t h e v o l u m e o f a s o l i d$ $b o u n d e d b y a s u r f a c e w i t h e q u a t i o n$ ${(x^{2} + y^{2} + z^{2})}^{2} = a^{3} x .$

Question Number 19666 Answers: 1 Comments: 0

∫ x^4 (√(x^2 + 1)) dx

$\int x^{4} \sqrt{x^{2} + 1} d x$

Question Number 19457 Answers: 1 Comments: 0

prove that ∫tan^2 xdx =tan x−x

$p r o v e t h a t \int \tan^{2} x d x$ $= \tan x - x$

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