Evaluate: | Basic Mathematics 2081

Basic Mathematics20815 marksNumerical: integral evaluationTrigonometric integrals

Evaluate: $\int \sqrt{4 - x^2} \, dx$ [5]

Evaluate: $$\int \sqrt{4 - x^2} , dx$$ [5]

Integral to evaluate: $\displaystyle \int \sqrt{4 - x^2}\, dx$ - Form: $\sqrt{a^2 - x^2}$ with $a^2 = 4 \Rightarrow a = 2$ Let $x = 2\sin\theta \Rightarrow dx = 2\cos\theta\, d\theta$ . Then: $\sqrt{4 - x^2} = \sqrt{4 - 4\sin^2\theta} = \sqrt{4\cos^2\theta} = 2\cos\theta$ $$\int \sqrt{4 - x^2}...

Integral to evaluate: $\displaystyle \int \sqrt{4 - x^2}, dx$ - Form: $\sqrt{a^2 - x^2}$ with $a^2 = 4 \Rightarrow a = 2$ Let $x = 2\sin\theta \Rightarrow dx = 2\cos\theta, d\theta$. Then: $$\sqrt{4 - x^2} = \sqrt{4 - 4\sin^2\theta} = \sqrt{4\cos^2\theta} = 2\cos\theta$$ $$\int \sqrt{4 - x^2}...