Question
Show that if $F ^ { \prime } ( x ) = G ^ { \prime } ( x )$ on $[ a , b ] ,$ then $F ( b ) - F ( a ) = G ( b ) - G ( a )$
Step 1
Step 1: Given that $F^{\prime}(x)=G^{\prime}(x)$, we can integrate both sides over the interval $[a, b]$ to get $\int_{a}^{b} F^{\prime}(x) d x=\int_{a}^{b} G^{\prime}(x) d x$. Show more…
Show all steps
Your feedback will help us improve your experience
Linh Vu and 51 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
If $f(x)=a^{x},$ show that $f(A+B)=f(A) \cdot f(B)$
Exponential and Logarithmic Functions
Exponential Functions
Show that $(f \circ g)(x)=(g \circ f)(x)=x$ $f(x)=a x+b ; \quad g(x)=\frac{1}{a}(x-b) \quad a \neq 0$
Composite Functions
show that $(f \circ g)(x)=(g \circ f)(x)=x$ $$ f(x)=a x+b ; g(x)=\frac{1}{a}(x-b) \quad a \neq 0 $$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD