No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
12[x2F(x)2−∫F(x)2d(x2)]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
12[x2F(x)−12∫(F(x))2dx]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Noneofthese
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B12[x2F(x)2−∫F(x)2d(x2)] ∫g(x)dx=f(x),∫x3g(x2)dxletx2=t⇒2xdx=dt,dx=dt2x⇒12∫tg(t)=t∫g(t)d−∫[dtdt.∫g(t)dt]dt⇒12∫g(t)=tf(t)−∫F(t)dt=12[x2F(x2)−∫F(x2)−dx2].