Integrate int01 x2 sqrtx3 + 1 dx | Mathematics I 2080

Mathematics I20805 marksNumerical: definite integralDefinite integral

Integrate $\int_0^1 x^2 \sqrt{x^3 + 1} dx$ [5]

Definite integral to evaluate: $\int0^1 x^2\sqrt{x^3+1}\, dx$ Lower limit $x=0$ , upper limit $x=1$ . Let $u = x^3 + 1$ . $\frac{du}{dx} = 3x^2 \implies du = 3x^2\, dx \implies x^2\, dx = \frac{du}{3}$ - $x = 0 \Rightarrow u = 0^3 + 1 = 1$ - $x = 1 \Rightarrow u = 1^3 + 1 = 2$ $$\int0^1 x^2\sqrt...

Definite integral to evaluate: $$\int0^1 x^2\sqrt{x^3+1}, dx$$ Lower limit $x=0$, upper limit $x=1$. Let $u = x^3 + 1$. $$\frac{du}{dx} = 3x^2 \implies du = 3x^2, dx \implies x^2, dx = \frac{du}{3}$$ - $x = 0 \Rightarrow u = 0^3 + 1 = 1$ - $x = 1 \Rightarrow u = 1^3 + 1 = 2$ $$\int0^1 x^2\sqrt...

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