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IntegrationQuestion and Answers: Page 202

Question Number 75102 Answers: 0 Comments: 0

show by integration that the centroid of a semi−circular lamina of radius a from the centre is ((4a)/(3π)).

$show by integration that the centroid$ $of a semi - circular lamina of radius a$ $from the centre is \frac{4 a}{3 π} .$

Question Number 75098 Answers: 1 Comments: 0

the function f is defined by f(x) = (2/(x^2 −1)) a) Express f into partial fraction b.show that ∫_3 ^5 f(x) dx = ln((4/3))

$the function f is defined by f (x) = \frac{2}{x^{2} - 1}$ $a) Express f into partial fraction$ $b . show that \int_{3}^{5} f (x) d x = l n (\frac{4}{3})$

Question Number 75093 Answers: 1 Comments: 1

∫cos^3 xsin^3 xdx

$\int {c o s}^{3} {x s i n}^{3} x d x$

Question Number 75082 Answers: 1 Comments: 0

find ∫_0 ^π e^(cosx) sinx dx

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

Question Number 75081 Answers: 1 Comments: 0

Evaluate ∫_1 ^(3 ) (x^2 /(1+x)) dx

$E v a l u a t e$ $\int_{1}^{3} \frac{x^{2}}{1 + x} d x$

Question Number 75034 Answers: 3 Comments: 0

Question Number 75027 Answers: 1 Comments: 1

Question Number 74997 Answers: 1 Comments: 1

Question Number 74995 Answers: 1 Comments: 1

find ∫_0 ^(π/2) Log cosx dx

$find \int_{0}^{\frac{π}{2}} Log \cos x d x$

Question Number 74891 Answers: 0 Comments: 4

Q. How will you define integrating constant C ? In how many ways can you define C ?

$Q . How will you define integrating$ $constant C ? In how many ways can you$ $define C ?$

Question Number 74890 Answers: 1 Comments: 1

find ∫ (x+3)(√((x−1)(2−x)))dx

$f i n d \int (x + 3) \sqrt{(x - 1) (2 - x)} d x$

Question Number 74889 Answers: 1 Comments: 1

find ∫_(−(1/2)) ^(+∞) e^(−x) (√(2x+1))dx

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

Question Number 74888 Answers: 1 Comments: 3

calculate f(α)=∫(√(x^2 −x+α))dx (α real)

$c a l c u l a t e f (α) = \int \sqrt{x^{2} - x + α} d x (α r e a l)$

Question Number 74886 Answers: 0 Comments: 1

calculate ∫ ((x+1)/((x^3 +x−2)^2 ))dx

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

Question Number 74861 Answers: 1 Comments: 0

Question Number 74799 Answers: 1 Comments: 0

prove that 0≤∫_0 ^∞ ((t^2 e^(−nt) )/(e^t −1))dt ≤(1/n^2 ) for n integr not 0

$p r o v e t h a t 0 ⩽ \int_{0}^{\infty} \frac{t^{2} e^{- n t}}{e^{t} - 1} d t ⩽ \frac{1}{n^{2}} f o r n i n t e g r n o t 0$

Question Number 74798 Answers: 0 Comments: 0

calculate ∫_0 ^π ln(1−2xcosθ +x^2 )dθ with ∣x∣<1

$c a l c u l a t e \int_{0}^{π} l n (1 - 2 x c o s θ + x^{2}) d θ w i t h ∣ x ∣< 1$

Question Number 74796 Answers: 0 Comments: 0

let U_n =(−1)^n {arcsin((1/n))−(1/n)}^(1/3) study the convergence of Σ U_n

$l e t U_{n} = {(- 1)}^{n} {a r c s i n (\frac{1}{n}) - \frac{1}{n}}^{\frac{1}{3}}$ $s t u d y t h e c o n v e r g e n c e o f Σ U_{n}$

Question Number 74793 Answers: 1 Comments: 1

prove the convergence of ∫_0 ^1 ((ln(1+(√x)))/(√x))dx

$p r o v e t h e c o n v e r g e n c e o f \int_{0}^{1} \frac{l n (1 + \sqrt{x})}{\sqrt{x}} d x$

Question Number 74720 Answers: 2 Comments: 5

Question Number 74944 Answers: 0 Comments: 0

∫(e^(−cos(2x)) /(sin^2 (x))) dx

$\int \frac{e^{- c o s (2 x)}}{{s i n}^{2} (x)} d x$

Question Number 74621 Answers: 1 Comments: 1

Question Number 74620 Answers: 1 Comments: 0

Question Number 74514 Answers: 1 Comments: 1

calculate ∫_0 ^(2π) (((x−sinθ)dθ)/((x^2 −2x sinθ +1)^2 ))

$c a l c u l a t e \int_{0}^{2 π} \frac{(x - s i n θ) d θ}{{(x^{2} - 2 x s i n θ + 1)}^{2}}$

Question Number 74500 Answers: 0 Comments: 0

1) decompose the fraction F(x)=((x^3 −2)/((x+1)^4 (x−2)^3 )) 2)find ∫_3 ^(+∞) F(x)dx

$1) d e c o m p o s e t h e f r a c t i o n F (x) = \frac{x^{3} - 2}{{(x + 1)}^{4} {(x - 2)}^{3}}$ $2) f i n d \int_{3}^{+ \infty} F (x) d x$

Question Number 74492 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(x^2 ))/(x^2 +9))dx

$c a l c u l a t e \int_{0}^{\infty} \frac{a r c t a n (x^{2})}{x^{2} + 9} d x$

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