Nursery calculus!

Calculus Level 1

$\large \displaystyle \int_0^x 4t^3\, dt = \ ?$

\dfrac {x^4} {4}

x^3

\dfrac{x^3}{3}

x^2

x^4

x^{\iota}

2 solutions

Caleb Townsend
Mar 16, 2015

$\int_0^x 4t^3\ dt = \frac{4}{3+1}t^{3+1} \bigg|_{0}^{x} = x^4 - 0^4 = \boxed{x^4}$

Daniel Ferreira
Aug 1, 2015

$\\ \int_{0}^{x} 4t^3 \, dt = \\\\\\ \left [ 4 \cdot \frac{t^4}{4} \right ]_{0}^{x}$

Using the Fundamental Theorem of Calculus,

$\\ F(x) - F(0) = \\\\ x^4 - 0^4 = \\\\ \boxed{\boxed{x^4}}$