Category: Integration

Question Number 216390 by jucimar last updated on 06/Feb/25 $$f\left(x\right)=ax$$ Commented by issac last updated on 07/Feb/25 $$f\left(x\right)=ax\dots .??$$ Commented by MrGaster…

Question Number 216281 by MrGaster last updated on 02/Feb/25 $$\mathrm{Prove}:{\int }_0^{\frac{\pi }{2}}d\varphi {\int }_0^{\frac{\pi }{2}}f\left(\sin \theta \cos \theta \right)\sin \theta d\theta =\frac{\pi }{2}{\int }_0^{1}f\left(x\right)dx$$ Commented by mr W last updated on…

Question Number 216042 by ajfour last updated on 26/Jan/25 $$\left(i\right)\int \sec {}^5\theta d\theta$$$$\left(ii\right)\int \frac{\sqrt{\tan \theta }d\theta }{\cos \theta }$$ Commented by ajfour last updated on 26/Jan/25 https://youtu.be/VqEdd_VGxGI?si=VnVRn7bW5wENyi9Y Find radius of circle inscribed in half ellipse. Commented by…

Question Number 215963 by RoseAli last updated on 23/Jan/25 Answered by Frix last updated on 23/Jan/25 $$\int {(\cos x+\sin x)}^n(1-{2\sin }^{2}x)dx=$$$$=\int\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)^{{n}} \left(\mathrm{sin}^{\mathrm{2}} \:{x}\:−\mathrm{cos}^{\mathrm{2}} \:{x}\right){dx}= \…

Question Number 215789 by universe last updated on 18/Jan/25 Commented by mr W last updated on 18/Jan/25 Answered by mr W last updated on 18/Jan/25…