Displaystyle int-0-1-frac-xdx-x-2-1-2-1-21-31-40

Question

Toppr Admin · Accepted Answer

-x222B-10xdx-x2-1-2-x222B-xdx-x2-1-2-12-x222B-dx2-1-x2-2-x2212-12-11-x2-x2212-1-x2212-12-1-x2-c-x222B-10xdx-x2-1-2-x2212-12-1-x2-c-x222B-10-x2212-12-2-c-x2212-x2212-12-c-x2212-14-12-14-x222B-10xdx-x2-1-2-14

Circles	Number of common tangents
I: $x^{2} + y^{2} = 4$ $x^{2} + y^{2} - 8 x + 12 = 0$	a) $0$
II: $x^{2} + y^{2} = 1$ $x^{2} + y^{2} - 2 x - 6 y + 6 = 0$	b) $1$
III: $x^{2} + y^{2} = 16$ $x^{2} + y^{2} - 8 x + 6 y - 56 = 0$	c) $4$
IV: $x^{2} + y^{2} - 2 x - 6 y + 9 = 0$ $x^{2} + y^{2} + 6 x - 2 y + 1 = 0$	d) $3$

∫10xdx(x2+1)2=1/21/31/40

∫10xdx(x2+1)2 ∫xdx(x2+1)2=12∫dx2(1+x2)2=−12(11+x2)−1 =−12(1+x2)+c =∫10xdx(x2+1)2=[−12(1+x2)+c]∫10 =[−12(2)+c]−[−12+c] =−14+12=14 ∫10xdx(x2+1)2=14

$\int_{0}^{1} \frac{x d x}{(x^{2} + 1)^{2}} =$

$1 / 2$
$1 / 3$
$1 / 4$
$0$