The Fundamental Theorem of Calculus says that f(x)dx = F(a) – F(b) provided f = F"...
(1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of (1 point) If f(x) dx 21 and g(x) dz 16, find [4f(z) +6g(a)] dz. Answer: 164 (1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of (1 point) If f(x) dx 21 and g(x) dz 16, find [4f(z) +6g(a)] dz. Answer: 164
Find the derivative using the fundamental Theorem of Calculus, part 1, which states that it (x) is continuous over an interval [a, 01, and the function FOX) is defined by FO) - , then F-xlover [a, b]
8. Use the Fundamental Theorem of Calculus to find F'(x) given F(x)= pos() In(t+1) 8. (5 points) Use the Fundamental Theorem of Calculus to find F"(x) given F(x) - KREME RE Juin(a) sec" (6)
Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 1 2 3 dx 1 2 3 dx √1-x² (Type an exact answer.) S 11
The Fundamental Theorem of Calculus tells us how we can calculate the anti-derivative of any function that is continuous on a closed interval. True False
Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 2 6 dx S √1-x² 0 V3 2 6 dx 5 0 V1 - (Type an exact answer.)
Theorem 20.8 (The Mean Value Theorem for Integral Calculus). Let f a, bR be continuous, and g a, bR be integrable and nonnegative. Then, there exists acE (a,b) such that (20.3) f(x)g(a)dx - f(c g(x)dr (ii). Apply Theorem 20.8 to show that 1 100 32 Jo (1 +r2)5 Theorem 20.8 (The Mean Value Theorem for Integral Calculus). Let f a, bR be continuous, and g a, bR be integrable and nonnegative. Then, there exists acE (a,b) such that (20.3) f(x)g(a)dx...
10. Use the Fundamental Theorem of Calculus to provide a proof of Theorem 8.4 under the additional assumption that each fis continuous on I la, b).(Hint: For x in la, b.o)If f g uniformly on [a, b], then Theorem 8.3 implies that im f.(x) f (x8. It follows that frpuintwise on la, b), where F(x) -lim frCro) + .By Theorem 6.12, F()-x) on la,b). Now show that f uniformly on la, b].] F heorem 8.4 Suppose that neN is a...
Use part I of the Fundamental Theorem of Calculus to find the derivative of F(x)=∫4 x sin(t3)dt F′(x) =
Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 2. 3 dx 2 (Type an exact answer.)