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IntegrationQuestion and Answers: Page 145

Question Number 107285 Answers: 0 Comments: 0

find ∫_0 ^1 ((arctan(2x))/(1+x^2 ))dx

$find \int_{0}^{1} \frac{\arctan (2 x)}{1 + x^{2}} dx$

Question Number 107283 Answers: 0 Comments: 0

f integrable continue on [a,b] let m =inf f(x) and M=sup f(x) (x ∈[a,b] prove that (b−a)^2 ≤∫_a ^b f(x)dx×∫_a ^b (dx/(f(x)))≤(((b−a)^2 )/4)(((m+M)^2 )/(mM))

$f integrable continue on [a, b] let m = \inf f (x) and M = \sup f (x)$ $(x \in [a, b] prove that {(b - a)}^{2} ⩽ \int_{a}^{b} f (x) dx \times \int_{a}^{b} \frac{dx}{f (x)} ⩽ \frac{{(b - a)}^{2}}{4} \frac{{(m + M)}^{2}}{mM}$

Question Number 107245 Answers: 0 Comments: 0

♣ Question♣ Why ??? ....∫_0 ^( (π/2)) (√((((2^x −1)sin^3 (x))/((2^x +1)(sin^3 (x)+cos^3 (x)))) ))<(π/8) ....M.N....

$♣ Q u e s t i o n ♣$ $W h y ? ? ?$ $. . . . \int_{0}^{\frac{π}{2}} \sqrt{\frac{(2^{x} - 1) {s i n}^{3} (x)}{(2^{x} + 1) ({s i n}^{3} (x) + {c o s}^{3} (x))}} < \frac{π}{8}$ $. . . . M . N . . . .$

Question Number 107212 Answers: 4 Comments: 0

⊚bemath⊚ ∫ x^6 (√(1−x^2 )) dx ?

$⊚ b e m a t h ⊚$ $\int x^{6} \sqrt{1 - x^{2}} d x ?$

Question Number 107238 Answers: 3 Comments: 0

⊞bemath⊞ ∫ ((sin x)/(sin^3 x+cos^3 x)) dx ?

$⊞ b e m a t h ⊞$ $\int \frac{\sin x}{\sin^{3} x + \cos^{3} x} d x ?$

Question Number 107197 Answers: 0 Comments: 0

⊵JS⊴ ∫ _0 ^( π/6) sin^2 (6x) cos^4 (3x) dx ? [ by using the Gamma function ]

$⊵ JS ⊴$ $\int {\overset{π / 6}{}}_{0} \sin^{2} (6 x) \cos^{4} (3 x) dx ?$ $[by using the G amma function]$

Question Number 107193 Answers: 1 Comments: 0

∫_0 ^4 ((ln x)/(√(4x−x^2 ))) dx ?

$\underset{0}{\int^{4}} \frac{\ln x}{\sqrt{4 x - x^{2}}} dx ?$

Question Number 107184 Answers: 2 Comments: 0

@bemath@ ∫_0 ^2 x ((8−x^3 ))^(1/3) dx =?

$@ b e m a t h @$ $\underset{0}{\int^{2}} x \sqrt[3]{8 - x^{3}} d x = ?$

Question Number 107162 Answers: 1 Comments: 1

Question Number 107141 Answers: 0 Comments: 0

∫(x^3 +x^6 )(((x^3 +2))^(1/3) )dx

$\int (x^{3} + x^{6}) (\sqrt[3]{x^{3} + 2}) d x$

Question Number 107113 Answers: 0 Comments: 0

Question Number 107107 Answers: 1 Comments: 2

Question Number 107036 Answers: 2 Comments: 1

∫ (((√(1+x^2 )) dx)/x^4 ) ?

$\int \frac{\sqrt{1 + x^{2}} dx}{x^{4}} ?$

Question Number 107002 Answers: 3 Comments: 0

∫_0 ^π ((cosx)/(√(2−sin^2 x)))dx

$\int_{0}^{π} \frac{cosx}{\sqrt{2 - \sin^{2} x}} dx$

Question Number 106964 Answers: 5 Comments: 4

∫_0 ^π ((sec^2 x)/(√(1−tan^2 x)))dx

$\int_{0}^{π} \frac{\sec^{2} x}{\sqrt{1 - \tan^{2} x}} dx$

Question Number 106948 Answers: 4 Comments: 0

let f(a) =∫_0 ^π (dx/(a+cos^2 x)) with a>0 1) explicite f(a) 2)explicite g(a) =∫_0 ^π (dx/((a+cos^2 x)^2 )) 3) find tbe valued of intevrsls ∫_0 ^π (dx/(1+cos^2 x)) and ∫_0 ^π (dx/((1+cos^2 x)^2 ))

$let f (a) = \int_{0}^{π} \frac{dx}{a + \cos^{2} x} with a > 0$ $1) explicite f (a)$ $2) explicite g (a) = \int_{0}^{π} \frac{dx}{{(a + \cos^{2} x)}^{2}}$ $3) find tbe valued of intevrsls$ $\int_{0}^{π} \frac{dx}{1 + \cos^{2} x} and \int_{0}^{π} \frac{dx}{{(1 + \cos^{2} x)}^{2}}$

Question Number 107051 Answers: 2 Comments: 0

∫_0 ^π ((cosx)/(2+sin^2 x))dx

$\int_{0}^{π} \frac{cosx}{2 + \sin^{2} x} dx$

Question Number 106932 Answers: 3 Comments: 0

∫_0 ^π (x/(1+cos^2 x))dx

$\int_{0}^{π} \frac{x}{1 + \cos^{2} x} dx$

Question Number 106908 Answers: 1 Comments: 0

Question Number 106899 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((tsin(2t))/(t^2 +4)) dt

$calculate \int_{0}^{\infty} \frac{tsin (2 t)}{t^{2} + 4} dt$

Question Number 106867 Answers: 2 Comments: 3

∀n∈(0, 1)∀x∈R : f(x) = (n/(n−1))x+n The given function gives a linear line that goes through points (0, n) and (1−n, 0). The function changes as n changes. What area is beneath the shape made as n goes from 0→1?

$\forall n \in (0, 1) \forall x \in R : f (x) = \frac{n}{n - 1} x + n$ $The given function gives a linear line that$ $goes through points (0, n) and (1 - n, 0) .$ $The function changes as n changes .$ $What area is beneath the shape made as$ $n goes from 0 \to 1 ?$

Question Number 106830 Answers: 1 Comments: 7

∫(( dx)/((√(x^3 )) ^3 (√(1 +^4 (√x^3 ))))) = ?

$\int \frac{d x}{\sqrt{x^{3}}^{3} \sqrt{1 +^{4} \sqrt{x^{3}}}} = ?$

Question Number 106809 Answers: 2 Comments: 0

∫e^(2x) sine^x dx=??

$\int e^{2 x} {s i n e}^{x} d x = ? ?$

Question Number 106808 Answers: 0 Comments: 0

∫tan(lnx)dx=???

$\int t a n (l n x) d x = ? ? ?$

Question Number 106807 Answers: 1 Comments: 0

∫sin(ln3x)dx=???

$\int s i n (l n 3 x) d x = ? ? ?$

Question Number 106782 Answers: 1 Comments: 0

∫2xdx

$\int 2 x d x$

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