Question
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.$$F(x)=\int_{x}^{x} \sqrt{1+\sec t} d t$$
Step 1
However, to apply the Fundamental Theorem of Calculus, we need to switch the limits of integration. This will introduce a negative sign in front of the integral. So, we rewrite the function as: $$F(x)=-\int_{x}^{x} \sqrt{1+\sec t} d t$$ Show more…
Show all steps
Your feedback will help us improve your experience
Adrian Co and 65 other Calculus 2 / BC 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
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. $F(x)=\int_{x}^{0} \sqrt{1+\sec t} d t$ $$\left[\operatorname{Hint} : \int_{x}^{0} \sqrt{1+\sec t} d t=-\int_{0}^{x} \sqrt{1+\sec t} d t\right]$$
Integrals
The Fundamental Theorem of Calculus
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. $ \displaystyle F(x) = \int^0_x \sqrt{1 + \sec t} \,dt $ $$ \biggl[ \textit{Hint:} \int^0_x \sqrt{1 + \sec t} \,dt = - \int^x_0 \sqrt{1 + \sec t} \,dt \biggr] $$
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.$G(x)=\int_{x}^{1} \cos \sqrt{t} d t$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD