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IntegrationQuestion and Answers: Page 304

Question Number 31073 Answers: 1 Comments: 1

find I= ∫_0 ^(π/2) ((1−sinθ)/(cosθ))dθ .

$f i n d I = \int_{0}^{\frac{π}{2}} \frac{1 - s i n θ}{c o s θ} d θ .$

Question Number 31072 Answers: 0 Comments: 0

find ∫_0 ^∞ (dx/(e^x (√(sh(2x))))) dx.

$f i n d \int_{0}^{\infty} \frac{d x}{e^{x} \sqrt{s h (2 x)}} d x .$

Question Number 31071 Answers: 1 Comments: 3

find ∫_0 ^π (dx/(1+sin^2 x)) .

$f i n d \int_{0}^{π} \frac{d x}{1 + {s i n}^{2} x} .$

Question Number 31070 Answers: 0 Comments: 1

calculate ∫_0 ^π (dx/(1+2cosx)) .

$c a l c u l a t e \int_{0}^{π} \frac{d x}{1 + 2 c o s x} .$

Question Number 31069 Answers: 1 Comments: 1

clculate ∫_0 ^1 x(√(x^2 −2x+2)) dx

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

Question Number 31068 Answers: 0 Comments: 0

find I_n =∫_(−(π/2)) ^(π/2) e^(−ax) cos^(2n) xdx .

$f i n d I_{n} = \int_{- \frac{π}{2}}^{\frac{π}{2}} e^{- a x} {c o s}^{2 n} x d x .$

Question Number 31067 Answers: 0 Comments: 0

find A_n =∫_0 ^∞ x^(2n) e^(−ax^2 ) dx.

$f i n d A_{n} = \int_{0}^{\infty} x^{2 n} e^{- {a x}^{2}} d x .$

Question Number 31066 Answers: 0 Comments: 0

find I_n =∫_0 ^(π/2) cos^(2n+1) xdx.

$f i n d I_{n} = \int_{0}^{\frac{π}{2}} {c o s}^{2 n + 1} x d x .$

Question Number 31065 Answers: 0 Comments: 0

find ∫_0 ^π ((xsinx)/((1−acosx)^2 )) dx with ∣a∣<1.

$f i n d \int_{0}^{π} \frac{x s i n x}{{(1 - a c o s x)}^{2}} d x w i t h ∣ a ∣< 1 .$

Question Number 31063 Answers: 0 Comments: 0

find f(t)= ∫_0 ^1 ln(1+tx^2 )dxfor t>−1

$f i n d f (t) = \int_{0}^{1} l n (1 + {t x}^{2}) d x f o r t > - 1$

Question Number 31062 Answers: 0 Comments: 0

find ∫_0 ^(π/2) e^x sinx cos^2 xdx.

$f i n d \int_{0}^{\frac{π}{2}} e^{x} s i n x {c o s}^{2} x d x .$

Question Number 31061 Answers: 0 Comments: 0

find ∫_0 ^(π/2) (sinθ −cosθ)ln(sinθ+cosθ)dθ.

$f i n d \int_{0}^{\frac{π}{2}} (s i n θ - c o s θ) l n (s i n θ + c o s θ) d θ .$

Question Number 31060 Answers: 0 Comments: 0

calculate by recurrence ∫_0 ^∞ ((lnx)/((1+x)^n ))dx with n≥2 .

$c a l c u l a t e b y r e c u r r e n c e \int_{0}^{\infty} \frac{l n x}{{(1 + x)}^{n}} d x w i t h n ⩾ 2 .$

Question Number 31059 Answers: 0 Comments: 0

find ∫_0 ^(π/2) cos(2θ)ln(tanθ)dθ.

$f i n d \int_{0}^{\frac{π}{2}} c o s (2 θ) l n (t a n θ) d θ .$

Question Number 31058 Answers: 0 Comments: 0

find ∫_0 ^∞ ((x arctanx)/((1+x^2 )^2 ))dx

$f i n d \int_{0}^{\infty} \frac{x a r c t a n x}{{(1 + x^{2})}^{2}} d x$

Question Number 31057 Answers: 0 Comments: 0

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

$f i n d \int_{0}^{1} \frac{\sqrt{1 + x^{2}} - \sqrt{1 - x^{2}}}{x^{2}} d x .$

Question Number 31056 Answers: 0 Comments: 1

find ∫_1 ^(+∞) (dx/(x^2 −2xcosα +1)) with 0<α<π .

$f i n d \int_{1}^{+ \infty} \frac{d x}{x^{2} - 2 x c o s α + 1} w i t h 0 < α < π .$

Question Number 31055 Answers: 0 Comments: 1

find ∫_(−∞) ^(+∞) (dx/((x^2 −x+1)(x^2 −2x+4))) .

$f i n d \int_{- \infty}^{+ \infty} \frac{d x}{(x^{2} - x + 1) (x^{2} - 2 x + 4)} .$

Question Number 31054 Answers: 0 Comments: 0

find ∫_0 ^1 (dx/(x^4 +1)) .

$f i n d \int_{0}^{1} \frac{d x}{x^{4} + 1} .$

Question Number 31053 Answers: 0 Comments: 1

let λ ∈R and a>0 find ∫_0 ^∞ e^(−ax) cos(λx)dx .

$l e t λ \in R a n d a > 0 f i n d \int_{0}^{\infty} e^{- a x} c o s (λ x) d x .$

Question Number 31052 Answers: 0 Comments: 0

let give 0<a<b find ∫_a ^b ((lnx)/x)dx .

$l e t g i v e 0 < a < b f i n d \int_{a}^{b} \frac{l n x}{x} d x .$

Question Number 31051 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ ((e^(−ax) −e^(−bx) )/(1− e^(−x) )) dx.

$s t u d y t h e c o n v e r g e n c e o f \int_{0}^{\infty} \frac{e^{- a x} - e^{- b x}}{1 - e^{- x}} d x .$

Question Number 31049 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ x^(−x) dx .

$s t u d y t h e c o n v e r g e n c e o f \int_{0}^{\infty} x^{- x} d x .$

Question Number 31048 Answers: 0 Comments: 0

study the convergence of ∫_1 ^(+∞) (((π/2) −arctanx)/x)dx

$s t u d y t h e c o n v e r g e n c e o f \int_{1}^{+ \infty} \frac{\frac{π}{2} - a r c t a n x}{x} d x$

Question Number 31145 Answers: 1 Comments: 0

Given ∫_0 ^1 f(x) dx = (((2018)),(( 0)) ) + (1/2) (((2018)),(( 1)) ) + (1/3) (((2018)),(( 2)) ) + ... + (1/(2019)) (((2018)),((2018)) ) ∫_0 ^1 g(x) dx = (((2018)),(( 0)) ) − (1/2) (((2018)),(( 1)) ) + (1/3) (((2018)),(( 2)) ) − ... + (1/(2019)) (((2018)),((2018)) ) h(x) is an odd function Then what is the value of ∫_(−3) ^( 3) f(x).g(x).h(x) dx ?

$Given$ $\int_{0}^{1} f (x) d x = (\begin{matrix} 2018 \\ 0 \end{matrix}) + \frac{1}{2} (\begin{matrix} 2018 \\ 1 \end{matrix}) + \frac{1}{3} (\begin{matrix} 2018 \\ 2 \end{matrix}) + . . . + \frac{1}{2019} (\begin{matrix} 2018 \\ 2018 \end{matrix})$ $\int_{0}^{1} g (x) d x = (\begin{matrix} 2018 \\ 0 \end{matrix}) - \frac{1}{2} (\begin{matrix} 2018 \\ 1 \end{matrix}) + \frac{1}{3} (\begin{matrix} 2018 \\ 2 \end{matrix}) - . . . + \frac{1}{2019} (\begin{matrix} 2018 \\ 2018 \end{matrix})$ $h (x) is an odd function$ $Then what is the value of \int_{- 3}^{3} f (x) . g (x) . h (x) d x ?$

Question Number 31141 Answers: 1 Comments: 0

using the limit defination find the area of f(x)= cos(x) [0,π/2]

$u s i n g t h e l i m i t d e f i n a t i o n$ $f i n d t h e a r e a o f$ $f (x) = c o s (x) [0, π / 2]$

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