Evaluate int03 sqrt1 + x2 cdot x3 , dx | Mathematics I 2081

Mathematics I20815 marksNumerical: definite integralDefinite integral

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

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

Integrand: $\sqrt{1+x^2}\cdot x^3$ - Limits: from $x=0$ to $x=3$ Let $u = 1+x^2$ , so $du = 2x\,dx$ , and $x^2 = u-1$ . Write $x^3\,dx = x^2\cdot x\,dx = (u-1)\cdot\dfrac{du}{2}$ . Limits: $x$ $u=1+x^2$ ---------------- $0$ $1$ $3$ $10$ $$\int0^3 \sqrt{1+x^2}\cdot x^3,dx = \frac{1}{2}\int1^{10}\sq...

Integrand: $\sqrt{1+x^2}\cdot x^3$ - Limits: from $x=0$ to $x=3$ Let $u = 1+x^2$, so $du = 2x,dx$, and $x^2 = u-1$. Write $x^3,dx = x^2\cdot x,dx = (u-1)\cdot\dfrac{du}{2}$. Limits: $x$ $u=1+x^2$ ---------------- $0$ $1$ $3$ $10$ $$\int0^3 \sqrt{1+x^2}\cdot x^3,dx = \frac{1}{2}\int1^{10}\sq...