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IntegrationQuestion and Answers: Page 151

Question Number 103040 Answers: 5 Comments: 0

given 5x+12y = 60 min value of (√(x^2 +y^2 ))

$g i v e n 5 x + 12 y = 60$ $m i n v a l u e o f \sqrt{x^{2} + y^{2}}$

Question Number 102987 Answers: 2 Comments: 0

lim_(x→0) ((x^2 sin (x^(−4) ))/x) ?

$\lim_{x \to 0} \frac{x^{2} \sin (x^{- 4})}{x} ?$

Question Number 102926 Answers: 3 Comments: 0

∫ (dθ/(2sin^2 θ−cos^2 θ)) ?

$\int \frac{d θ}{2 {s i n}^{2} θ - {c o s}^{2} θ} ?$

Question Number 102922 Answers: 1 Comments: 1

∫ (dx/(x^3 +3x−5)) ?

$\int \frac{d x}{x^{3} + 3 x - 5} ?$

Question Number 103071 Answers: 0 Comments: 0

∫(e^x /((1+x^2 )^2 ))∙(x^3 −x^2 +x+1)dx

$\int \frac{e^{x}}{{(1 + x^{2})}^{2}} \cdot (x^{3} - x^{2} + x + 1) dx$

Question Number 102911 Answers: 2 Comments: 1

∫ ((sin(x))/x) dx

$\int \frac{\sin (x)}{x} dx$

Question Number 102905 Answers: 1 Comments: 0

I=2∫_0 ^(1/(√2)) ((sin^(−1) (x))/x) dx −∫_0 ^1 ((tan^(−1) (x))/x)dx

$I = 2 \underset{0}{\int^{\frac{1}{\sqrt{2}}}} \frac{\sin^{- 1} (x)}{x} d x - \underset{0}{\int^{1}} \frac{\tan^{- 1} (x)}{x} d x$

Question Number 102790 Answers: 1 Comments: 0

I=2∫_0 ^(1/(√2)) ((sin^(−1) (x))/x) dx −∫_0 ^1 ((tan^(−1) (x))/x) dx

$I = 2 \underset{0}{\int^{\frac{1}{\sqrt{2}}}} \frac{\sin^{- 1} (x)}{x} d x - \underset{0}{\int^{1}} \frac{\tan^{- 1} (x)}{x} d x$

Question Number 102894 Answers: 3 Comments: 0

∫ (√(x+(√(x+(√(x+(√(x+(√(x+...)))))))))) dx

$\int \sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x + . . .}}}}} dx$

Question Number 102698 Answers: 2 Comments: 0

Question Number 102690 Answers: 3 Comments: 0

(1)∫(1/(cos (√x))) dx (2) ∫ (1/(2+cot x)) dx (3) ∫ (1/(ln(cos x))) dx

$(1) \int \frac{1}{\cos \sqrt{x}} dx$ $(2) \int \frac{1}{2 + \cot x} dx$ $(3) \int \frac{1}{\ln (\cos x)} dx$

Question Number 102606 Answers: 2 Comments: 1

what is the volume of region bounded by y =x^2 −2x and y=x that is rotated about y=4 ?

$w h a t i s t h e v o l u m e o f r e g i o n$ $b o u n d e d b y y = x^{2} - 2 x a n d$ $y = x t h a t i s r o t a t e d a b o u t$ $y = 4 ?$

Question Number 102470 Answers: 1 Comments: 0

∫(dx/(x^(10) +x^2 ))

$\int \frac{d x}{x^{10} + x^{2}}$

Question Number 102462 Answers: 8 Comments: 0

Calculate ; J=∫(dx/(x(x^2 +x−1)^2 )) K=∫((x^3 +x−1)/((x^2 +2)^2 ))dx L=∫(dx/(x+(√(x^2 +1))))

$Calculate;$ $J = \int \frac{dx}{x {(x^{2} + x - 1)}^{2}}$ $K = \int \frac{x^{3} + x - 1}{{(x^{2} + 2)}^{2}} dx$ $L = \int \frac{dx}{x + \sqrt{x^{2} + 1}}$

Question Number 102555 Answers: 0 Comments: 0

∫_0 ^1 ((x^(98) −99x+98)/(logx))dx

$\int_{0}^{1} \frac{x^{98} - 99 x + 98}{l o g x} d x$

Question Number 102417 Answers: 3 Comments: 0

calculate ∫_0 ^∞ e^(−x) ln(1+e^x )dx

$calculate \int_{0}^{\infty} e^{- x} \ln (1 + e^{x}) dx$

Question Number 102416 Answers: 2 Comments: 0

calculate ∫_0 ^1 e^(−x) ln(1+e^x )dx

$calculate \int_{0}^{1} e^{- x} \ln (1 + e^{x}) dx$

Question Number 102397 Answers: 0 Comments: 0

∫ln(x−(√x)+1)dx

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

Question Number 102383 Answers: 0 Comments: 2

∫(x/(sin^2 x−3))

$\int \frac{x}{{s i n}^{2} x - 3}$

Question Number 102381 Answers: 0 Comments: 0

∫((x(√6)sec^2 (x/2))/(1+9tan^4 (x/2)+18tan^2 (x/2)))dx

$\int \frac{x \sqrt{6} {s e c}^{2} \frac{x}{2}}{1 + 9 {t a n}^{4} \frac{x}{2} + 18 {t a n}^{2} \frac{x}{2}} d x$

Question Number 102369 Answers: 3 Comments: 0

find the area bounded inner the curve r = 4−2cos θ and outer the curve r = 6+2cos θ

$f i n d t h e a r e a b o u n d e d i n n e r t h e c u r v e$ $r = 4 - 2 \cos θ a n d o u t e r t h e c u r v e r = 6 + 2 \cos θ$

Question Number 102341 Answers: 4 Comments: 0

∫((xdx)/((1+x^2 )(√(1−x^2 ))))

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

Question Number 102366 Answers: 3 Comments: 0

∫_0 ^(π/2) ((cos x)/(1+cos x+sin x)) dx ?

$\underset{0}{\int^{π / 2}} \frac{\cos x}{1 + \cos x + \sin x} d x ?$

Question Number 102303 Answers: 2 Comments: 1

∫ ((1+csc 2x)/(1−sin 2x)) dx ?

$\int \frac{1 + \csc 2 x}{1 - \sin 2 x} d x ?$

Question Number 102330 Answers: 0 Comments: 0

Do this integration(please do it step by step and write the used formula) ∫(1/2)(sin x)(e^(sin x) )dx

$D o t h i s i n t e g r a t i o n (p l e a s e d o i t s t e p b y s t e p a n d w r i t e t h e u s e d f o r m u l a)$ $\int \frac{1}{2} (s i n x) (e^{s i n x}) d x$

Question Number 102275 Answers: 0 Comments: 2

∫_1 ^2 ln(((x^4 + 4)/(x^2 + 4)))(dx/x)

$\int_{1}^{2} l n (\frac{x^{4} + 4}{x^{2} + 4}) \frac{d x}{x}$

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