Evaluate $\frac{d}{d x} \int_{0}^{x}\left(e^{\arccos t}\right) d t$
A) $e^{\arccos x}$
B) $e^{\arccos t}$
C) $x$
D) $e^{x}-\arccos x$
E) $e^{\operatorname{arccost} \frac{x}{4}}$

Question

Quizplus · Accepted Answer

According to the fundamental theorem of calculus, if $F(x) = \int_{a(x)}^{b(x)} g(t) dt$, then $F'(x) = g(b(x)) \cdot b'(x) - g(a(x)) \cdot a'(x)$. In this case, we have $F(x) = \int_{0}^{x} e^{\arccos t} dt$, so $F'(x) = e^{\arccos x} \cdot 1 - e^{\arccos 0} \cdot 0 = e^{\arccos x}$. Therefore, the answer is (A).

Evaluate ddx∫0x(earccos⁡t)dt\frac{d}{d x} \int_{0}^{x}\left(e^{\arccos t}\right) d tdxd​∫0x​(earccost)dt A) earccos⁡xe^{\arccos x}earccosx B) earccos⁡te^{\arccos t}earccost

Evaluate $\frac{d}{d x} \int_{0}^{x}\left(e^{\arccos t}\right) d t$ A) $e^{\arccos x}$ B) $e^{\arccos t}$