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IntegrationQuestion and Answers: Page 192

Question Number 82700 Answers: 1 Comments: 4

∫ ((2dx)/(3x(√(5x^2 +6)))) ?

$\int \frac{2 d x}{3 x \sqrt{5 x^{2} + 6}} ?$

Question Number 82617 Answers: 1 Comments: 0

∫sin (101x)(sinx)^(99) dx

$\int \sin (101 x) {(s i n x)}^{99} d x$

Question Number 82614 Answers: 1 Comments: 0

∫ ((sin 2x)/(sin 5x sin 3x)) dx ?

$\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} d x ?$

Question Number 82685 Answers: 0 Comments: 0

∫_0 ^5 (((3x^3 −x^4 ))^(1/4) /(5−x))dx

$\int_{0}^{5} \frac{\sqrt[4]{3 x^{3} - x^{4}}}{5 - x} d x$

Question Number 82604 Answers: 1 Comments: 0

∫ ((cos (5x)+cos (4x) dx)/(1−2cos (3x))) =

$\int \frac{\cos (5 x) + \cos (4 x) d x}{1 - 2 \cos (3 x)} =$

Question Number 82577 Answers: 0 Comments: 3

∫((2−(√(x+3)))/(2+(√(x−3)))) dx

$\int \frac{2 - \sqrt{x + 3}}{2 + \sqrt{x - 3}} d x$

Question Number 82573 Answers: 0 Comments: 4

Question Number 82571 Answers: 0 Comments: 0

Question Number 82568 Answers: 1 Comments: 0

∫ (1/(tan x+cot x+sec x+cosec x)) dx ?

$\int \frac{1}{\tan x + \cot x + \sec x + cosec x} d x ?$

Question Number 82566 Answers: 2 Comments: 1

∫ (√((x+1)/x)) dx = ?

$\int \sqrt{\frac{x + 1}{x}} d x = ?$

Question Number 82560 Answers: 1 Comments: 0

Use gamma function to prove (i) ∫_0 ^(π/4) sin^4 x 2x dx = ((3𝛑−4)/(192)). (ii) ∫_0 ^(π/6) cos^4 3𝛉 sin^2 6θ = ((5π)/(192)).

$U se gamma function to prove$ $(i) \int_{0}^{\frac{π}{4}} \sin^{4} x 2 x dx = \frac{3 π - 4}{192} .$ $(ii) \int_{0}^{\frac{π}{6}} \cos^{4} 3 θ \sin^{2} 6 θ = \frac{5 π}{192} .$

Question Number 82531 Answers: 1 Comments: 1

Question Number 82510 Answers: 1 Comments: 1

∫ (√(x+(√x) )) dx = ?

$\int \sqrt{x + \sqrt{x}} d x = ?$

Question Number 82450 Answers: 1 Comments: 1

∫_0 ^π (1/(1+(tan(x))^(√2) )) dx

$\int_{0}^{π} \frac{1}{1 + {(t a n (x))}^{\sqrt{2}}} d x$

Question Number 82446 Answers: 0 Comments: 3

show that ∫_0 ^∞ x^(−log(x)) x log(x) dx=e(√π)

$s h o w t h a t$ $\int_{0}^{\infty} x^{- l o g (x)} x l o g (x) d x = e \sqrt{π}$

Question Number 82440 Answers: 0 Comments: 1

find ∫ ((x+1)/(x+2))(√((1−x)/(1+x)))dx

$f i n d \int \frac{x + 1}{x + 2} \sqrt{\frac{1 - x}{1 + x}} d x$

Question Number 82439 Answers: 0 Comments: 1

calculate I_n =∫_0 ^1 x^n (√(1+x+x^2 ))dx

$c a l c u l a t e I_{n} = \int_{0}^{1} x^{n} \sqrt{1 + x + x^{2}} d x$

Question Number 82442 Answers: 0 Comments: 1

1)find ∫ ((√(x^2 −x+1))/(x^2 +3))dx 2)calculate ∫_0 ^1 ((√(x^2 −x+1))/(x^2 +3))dx

$1) f i n d \int \frac{\sqrt{x^{2} - x + 1}}{x^{2} + 3} d x$ $2) c a l c u l a t e \int_{0}^{1} \frac{\sqrt{x^{2} - x + 1}}{x^{2} + 3} d x$

Question Number 82435 Answers: 0 Comments: 1

calculate ∫_4 ^(+∞) (x^3 /((2x+1)^3 (x−3)^5 ))dx

$c a l c u l a t e \int_{4}^{+ \infty} \frac{x^{3}}{{(2 x + 1)}^{3} {(x - 3)}^{5}} d x$

Question Number 82434 Answers: 0 Comments: 0

1)decompose inside C(x)and R(x) the fraction F(x)=((2x+1)/((x^2 +1)^3 (x−1)^2 )) 2) find the value of ∫_3 ^(+∞) F(x)dx

$1) d e c o m p o s e i n s i d e C (x) a n d R (x) t h e f r a c t i o n$ $F (x) = \frac{2 x + 1}{{(x^{2} + 1)}^{3} {(x - 1)}^{2}}$ $2) f i n d t h e v a l u e o f \int_{3}^{+ \infty} F (x) d x$

Question Number 82433 Answers: 0 Comments: 1

1)decompose inside C(x)and R(x) F=(1/((x^2 +x+1)^2 )) 2)calculate ∫_0 ^∞ (dx/((x^2 +x+1)^2 ))

$1) d e c o m p o s e i n s i d e C (x) a n d R (x) F = \frac{1}{{(x^{2} + x + 1)}^{2}}$ $2) c a l c u l a t e \int_{0}^{\infty} \frac{d x}{{(x^{2} + x + 1)}^{2}}$

Question Number 82402 Answers: 0 Comments: 0

Question Number 82391 Answers: 0 Comments: 1

∫ sin x cos (sin x) dx ?

$\int \sin x \cos (\sin x) d x ?$

Question Number 82330 Answers: 0 Comments: 4

Question Number 82286 Answers: 1 Comments: 3

1) find a and b wich verify ∫_0 ^π (at^2 +bt)cos(nx) =(1/n^2 ) 2) find the value of Σ_(n=1) ^∞ (1/n^2 )

$1) f i n d a a n d b w i c h v e r i f y \int_{0}^{π} ({a t}^{2} + b t) c o s (n x) = \frac{1}{n^{2}}$ $2) f i n d t h e v a l u e o f \sum_{n = 1}^{\infty} \frac{1}{n^{2}}$

Question Number 82283 Answers: 1 Comments: 2

∫x^3 (√(x^3 +1)) dx

$\int x^{3} \sqrt{x^{3} + 1} d x$

Pg 187 Pg 188 Pg 189 Pg 190 Pg 191 Pg 192 Pg 193 Pg 194 Pg 195 Pg 196

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