Question and Answers Forum

(a) Evaluate the integral of the function: y(x) = ((3x + 1)/(2x^2 − 2x + 3)) (b) Find the constant A, B, C in the identity: ((3x^2 − ax)/((x − 2a)(x^2 + a^2 ))) ≡ (A/((x − 2a))) + ((Bx + Ca)/((x^2 + a^2 ))) where a is a constant, hence prove that. ∫_0 ^( 2) ((3x^2 − ax)/((x − 2a)(x^2 + a^2 ))) dx = (π/4) − (3/2) ln(2)

$(a) Evaluate the integral of the function : y (x) = \frac{3 x + 1}{{2 x}^{2} - 2 x + 3}$ $(b) Find the constant A, B, C in the identity :$ $\frac{{3 x}^{2} - ax}{(x - 2 a) (x^{2} + a^{2})} \equiv \frac{A}{(x - 2 a)} + \frac{Bx + Ca}{(x^{2} + a^{2})}$ $where a is a constant, hence prove that .$ $\int_{0}^{2} \frac{{3 x}^{2} - ax}{(x - 2 a) (x^{2} + a^{2})} dx = \frac{π}{4} - \frac{3}{2} \ln (2)$

Question Number 18024 Answers: 2 Comments: 0

Question Number 17909 Answers: 0 Comments: 1

Please answer Q. 17525

$P l e a s e a n s w e r Q . 17525$

Question Number 17736 Answers: 0 Comments: 1

evaluate; ∫ln (sin 2x)dx

$e v a l u a t e; \int \ln (\sin 2 x) d x$

Question Number 17676 Answers: 2 Comments: 0

Question Number 17625 Answers: 1 Comments: 1

Find the fourier series of : f(x) = x, from 0 < x < π

$Find the fourier series of : f (x) = x, from 0 < x < π$

Question Number 17604 Answers: 2 Comments: 0

∫_( 0) ^( n) x^2 (n − x)^p dx for p > 0

$\int_{0}^{n} x^{2} {(n - x)}^{p} dx for p > 0$

Question Number 17599 Answers: 1 Comments: 0

a particle starts with an initial speed u,it moves in a straight line with an accleration which varies as the square of the time the particle has been in motion. Find the speed at any time t,and the distance travelled.

$a particle starts with an initial$ $speed u, it moves in a straight$ $line with an accleration which$ $varies as the square of the time$ $the particle has been in motion .$ $Find the speed at any time t, and$ $the distance travelled .$

Question Number 17603 Answers: 2 Comments: 0

∫_( 0) ^( a/2) x^2 (a^2 − x^2 )^(3/2) dx

$\int_{0}^{a / 2} x^{2} {(a^{2} - x^{2})}^{\frac{3}{2}} dx$

Question Number 17525 Answers: 0 Comments: 1

Evaluate ∫_(−1) ^1 (1−x^2 )^(n/2) dx for n ∈ Z∩[0;∞) (i.e. 0, 1, 2, ...) and: a) n ≡ 0(mod 2) b) n ≡ 1(mod 2)

$Evaluate \underset{- 1}{\int^{1}} {(1 - x^{2})}^{\frac{n}{2}} d x for$ $n \in Z \cap [0; \infty) (i . e . 0, 1, 2, . . .) and :$ $a) n \equiv 0 (m o d 2)$ $b) n \equiv 1 (m o d 2)$

Question Number 17522 Answers: 0 Comments: 1

∫(dx/(sin^5 x+cos^5 x))

$\int \frac{d x}{\sin^{5} x + \cos^{5} x}$

Question Number 17514 Answers: 1 Comments: 2

S(n)=∫_0 ^1 x^(2n) sin(2nπx)dx

$S (n) = \int_{0}^{1} x^{2 n} s i n (2 n π x) d x$

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