If x-6 y-43 y2-4 y-3- then - x d y will be

Given x = (6y + 4) (3y^2 + 4y +3) Let t = 3y^2 + 4y + 3 Differentiating w.r.t. to y, dtdy =(6y + 4) ⇒ (6y + 4) dy = dt Multiplying both sides with (6y + 4) (3y ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Definite Integrals

If x=6 y+43 y...

Question

If $x = (6 y + 4) (3 y^{2} + 4 y + 3)$ , then $\int x d y$ will be

\frac{1}{3 y^{2} + 4 y + 3} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{(3 y^{2} + 4 y + 3)^{2}}{2} + C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 y^{2} + 4 y + 3 + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{(6 y + 4)}{3 y^{2} + 4 y + 3} + C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{(3 y^{2} + 4 y + 3)^{2}}{2} + C$
Given $x = (6 y + 4) (3 y^{2} + 4 y + 3)$
Let $t = 3 y^{2} + 4 y + 3$
Differentiating w.r.t. to $y$ ,
$\frac{d t}{d y} = (6 y + 4)$
$\Rightarrow (6 y + 4) d y = d t$

Multiplying both sides with $(6 y + 4) (3 y^{2} + 4 y + 3)$

$\Rightarrow (6 y + 4) (3 y^{2} + 4 y + 3) d y = (3 y^{2} + 4 y + 3) d t$
$∴ \int x d y = \int t d t = \frac{t^{2}}{2} + C = \frac{(3 y^{2} + 4 y + 3)^{2}}{2} + C$

Suggest Corrections

If x=(6y+4)(3y2+4y+3), then ∫xdy will be

The correct option is B (3y2+4y+3)22+CGiven x=(6y+4)(3y2+4y+3) Let t=3y2+4y+3 Differentiating w.r.t. to y, dtdy=(6y+4) ⇒(6y+4)dy=dt Multiplying both sides with (6y+4)(3y2+4y+3) ⇒(6y+4)(3y2+4y+3)dy=(3y2+4y+3)dt ∴∫xdy=∫tdt=t22+C=(3y2+4y+3)22+C

If $x = (6 y + 4) (3 y^{2} + 4 y + 3)$ , then $\int x d y$ will be