Question
If Φ(x)=∫dxsin12x cos72x, then Φ(π4)−Φ(0)=
Answer: Option A
:
A
tanx=t⇒sec2xdx=dt∴f(x)=∫dxsin12xcos12x.cos4x=∫(1+tan2x)sec2x√tanxdx=∫(1+t2)√tdt=∫(t−1/2+t3/2)dt=2t1/2+25t5/2=2√tanx+25(tanx)5/2∴ϕ(π4)−ϕ(0)=2+25=125
Was this answer helpful ?
:
A
tanx=t⇒sec2xdx=dt∴f(x)=∫dxsin12xcos12x.cos4x=∫(1+tan2x)sec2x√tanxdx=∫(1+t2)√tdt=∫(t−1/2+t3/2)dt=2t1/2+25t5/2=2√tanx+25(tanx)5/2∴ϕ(π4)−ϕ(0)=2+25=125
Was this answer helpful ?
More Questions on This Topic :
Question 2. ∫x2−2x3√x2−1dx is equal to....
Question 4. ∫(1+√tanx)(1+tan2x)2tanxdx equal to ....
Question 8. ∫dxcos(2x)cos(4x)is equal to....
Question 9. ∫ex[x3+x+1(1+x2)3/2]dx is equal to....
Question 10. ∫dxsin4x+cos4x is equal to....
Submit Solution