Fundamental Theorem of Calculus:
The fundamental theorem of calculus has two statements. The first statement states that if f is a continuous function on the closed interval [a, b] and A(x) be the area function. Then A′(x) = f(x), for all x ∈ [a, b].
And the second statement states that the function “f” is continuous on the closed interval [a, b], and F is an indefinite integral of a function “f” on [a, b], then the second fundamental theorem of calculus is defined as: F(b) – F(a) = 
Fundamental Theorem of Calculus Sample Questions:
Question 1: Calculate
(a) 30.5
(b) 34
(c) 21
(d) 40.5
Answer: (a)
Explanation: Let I =
Question 2: Find
(a) -10
(b) 9
(c) 10
(d) -9
Answer: (c)
Explanation: I =
Question 3: If 
(a)
(b)
(c)
(d)
Answer: (c)
Explanation: We are looking for the value of c such that,
f(c)= 
Question 4: Find the derivative of
g(x)=
(a)
(b)
(c)
(d)
Answer: (b)
Explanation: According to the Fundamental Theorem of Calculus, the derivative is given by g′(x)
Question 5: Calculate
(a)
(b)
(c)
(d)
Answer: (a)
Explanation: Let cos x=t
Differentiating w.r.t x, we get
sin x dx=dt
Question 6: Find
(a) -63
(b) -75
(c) 73
(d) 75
Answer: (b)
Explanation: Applying the limits by using the fundamental theorem of calculus.
Question 7: Calculate
(a) log 2
(b) log3
(c) 2 log2
(d) 0
Answer: (a)
Explanation: Apply the fundamental theorem of calculus.
Question 8: Find
(a)
(b) 4e
(c) -4e
(d) None
Answer: (a)
Explanation: Apply the fundamental theorem of calculus.
Question 9: Find
(a)
(b) 6
(c)
(d)
Answer: (c)
Explanation: Apply the limits.
Question 10: Find
(a)
(b)
(c)
(d)
Answer: (d)
Explanation: Apply the limits.