Let $f ( x ) = \int _ { 0 } ^ { 5 } t ^ { 4 } d t . \text { Find } f ^ { \prime } ( x )$
A)0
B) $2 x ^ { 6 }$
C) $18 x ^ { 8 }$
D) $x ^ { 6 }$
E) $2 x ^ { 2 }$
F) $x ^ { 4 }$
G) $12 x ^ { 5 }$
H) $2 x ^ { 9 }$

Question

Let $f ( x ) = \int _ { 0 } ^ { 5 } t ^ { 4 } d t . \text { Find } f ^ { \prime } ( x )$ 
A)0
B) $2 x ^ { 6 }$
C) $18 x ^ { 8 }$
D) $x ^ { 6 }$
E) $2 x ^ { 2 }$ 
F) $x ^ { 4 }$  
G) $12 x ^ { 5 }$  
H) $2 x ^ { 9 }$

Quizplus · Accepted Answer

The integral given, $\int _ { 0 } ^ { 5 } t ^ { 4 } d t$, is a definite integral with constant limits of integration (0 and 5). Therefore, it evaluates to a constant value. The derivative of a constant is 0, which means $f'(x) = 0$.

Let f(x)=∫05t4dt. Find f′(x)f ( x ) = \int _ { 0 } ^ { 5 } t ^ { 4 } d t . \text { Find } f ^ { \prime } ( x )f(x)=∫05​t4dt. Find f′(x)

Let $f ( x ) = \int _ { 0 } ^ { 5 } t ^ { 4 } d t . \text { Find } f ^ { \prime } ( x )$