Evaluate the integral using the Fundamental Theorem of Calculus, part 2, which states that if f is continuous over the interval [a, b] and F(x) is any antiderivative of f(x), then ?[a to b] f(x) dx = F(b) - F(a). ?[1/4 to 1] 32/x^3 dx
Added by Mario B.
Close
Step 1
Once we have that, we can find an antiderivative F(x) of f(x) and use the Fundamental Theorem of Calculus to evaluate the integral. For example, let's evaluate the integral ∫_0^2 x^2 dx. Here, f(x) = x^2 and the limits of integration are [0, 2]. Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 69 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
Find the derivative using the Fundamental Theorem of Calculus, part 1, which states that if f(x) is continuous over an interval [a, b], and the function F(x) is defined by F(x) = ∫(a to x) f(t) dt, then F '(x) = f(x) over [a, b]. d/dx (∫(a to 5x) f(t) dt)
Carson M.
Part 1 of the Fundamental Theorem of Calculus states that If f(x) is continuous on [a,b], the area function A(x) = ∫_a^x f(t)dt, for a ≤ x ≤ b, then d/dx ∫_a^x f(t)dt = __________. Part 2 of the Fundamental Theorem of Calculus states that If f(x) is continuous on [a,b] and F is any antiderivative of f(x) on [a,b], Then ∫_a^b f(x)dx = __________.
Sri K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD