Find $\frac{d}{d x} \int_{x}^{1}(1+t)^{3} d t$ .
A) $(1+x)^{3}$
B) $-(1+x)^{3}$
C) $\frac{1}{3}(1+x)^{4}$
D) $\frac{1}{3}(1+x)^{4}-\frac{16}{3}$

Name: Find $\frac{d}{d x} \int_{x}^{1}(1+t)^{3} d t$ . A) $(1+x)^{3}$ B) $-(1+x)^{3}$ C) $\frac{1}{3}(1+x)^{4}$ D) $\frac{1}{3}(1+x)^{4}-\frac{16}{3}$
Brand: Quizplus
Rating: 4.9 (36 reviews)

Question

Quizplus · Accepted Answer

The derivative of an integral with respect to its upper limit minus the derivative with respect to its lower limit gives $-(1+x)^3$, according to the Fundamental Theorem of Calculus.

Find ddx∫x1(1+t)3dt\frac{d}{d x} \int_{x}^{1}(1+t)^{3} d tdxd​∫x1​(1+t)3dt A) (1+x)3(1+x)^{3}(1+x)3 B) −(1+x)3-(1+x)^{3}−(1+x)3 C) 13(1+x)4\frac{1}{3}(1+x)^{4}31​(1+x)4 D) 13(1+x)4−163\frac{1}{3}(1+x)^{4}-\frac{16}{3}31​(1+x)4−316​

Find $\frac{d}{d x} \int_{x}^{1}(1+t)^{3} d t$
A) $(1+x)^{3}$ B) $-(1+x)^{3}$ C) $\frac{1}{3}(1+x)^{4}$ D) $\frac{1}{3}(1+x)^{4}-\frac{16}{3}$