Integrate the following: | Basic Mathematics 2077

Basic Mathematics20775 marksNumerical: integrationTrigonometric integrals

Integrate the following: $\int_{0}^{\frac{\pi}{4}} \frac{dx}{1-\sin x}$ [5]

Integrate the following: $$\int_{0}^{\frac{\pi}{4}} \frac{dx}{1-\sin x}$$ [5]

Integrand: $\dfrac{1}{1-\sin x}$ - Limits: from $0$ to $\dfrac{\pi}{4}$ (the LaTeX "x/4" is a rendering artifact for the standard upper limit $\pi/4$ ) $I = \int{0}^{\pi/4} \frac{dx}{1-\sin x}$ Multiply numerator and denominator by the conjugate $(1+\sin x)$ : $$I = \int{0}^{\pi/4} \frac{1+\sin...

Integrand: $\dfrac{1}{1-\sin x}$ - Limits: from $0$ to $\dfrac{\pi}{4}$ (the LaTeX "x/4" is a rendering artifact for the standard upper limit $\pi/4$) $$I = \int{0}^{\pi/4} \frac{dx}{1-\sin x}$$ Multiply numerator and denominator by the conjugate $(1+\sin x)$: $$I = \int{0}^{\pi/4} \frac{1+\sin...