2. Consider the curve y = sinx - on the inteval 0 ≤ x ≤ π/2. (a) Sketch the curve and shade in the region between the curve and the x axis. (b) Find the total area bounded between the curve and the x-axis on the interval 0≤x≤/2. (Hint: if you got 1-4≈ 0.2146 as the area, your answer is wrong. Try again.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 58E
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Question 2 only please. 

Math 151 Workshop 10 (Fundamental Theorem of Calculus
1. The graph of f is shown to the right. The function F(x) is
X
defined
F and f are different symbols, and they refer to different
functions.)
(a) Find F(0) and F(3).
(b) Find F'(1). (Yes, F'(1) does exist.)
(c) For what value of a does F(x) have its maximum value?
What is this maximum value?
X
by F(x) = f(t) dt for 0 ≤ x ≤ 4. (And note that
2. Consider the curve y = sin x
3. Find the following derivatives:
d
(a) / 2 sin (1²) dt.
da
f(t)
d
dx
(b) √2 cos (t²) dt.
3
2
0
21 3₁
= sinx - on the inteval 0 ≤ x ≤ π/2.
(a) Sketch the curve and shade in the region between the curve and the x axis.
(b) Find the total area bounded between the curve and the x-axis on the interval 0 ≤x≤ π/2.
(Hint: if you got 1
you got 1 - ≈ 0.2146 as the area, your answer is wrong. Try again.)
4
t
Transcribed Image Text:Math 151 Workshop 10 (Fundamental Theorem of Calculus 1. The graph of f is shown to the right. The function F(x) is X defined F and f are different symbols, and they refer to different functions.) (a) Find F(0) and F(3). (b) Find F'(1). (Yes, F'(1) does exist.) (c) For what value of a does F(x) have its maximum value? What is this maximum value? X by F(x) = f(t) dt for 0 ≤ x ≤ 4. (And note that 2. Consider the curve y = sin x 3. Find the following derivatives: d (a) / 2 sin (1²) dt. da f(t) d dx (b) √2 cos (t²) dt. 3 2 0 21 3₁ = sinx - on the inteval 0 ≤ x ≤ π/2. (a) Sketch the curve and shade in the region between the curve and the x axis. (b) Find the total area bounded between the curve and the x-axis on the interval 0 ≤x≤ π/2. (Hint: if you got 1 you got 1 - ≈ 0.2146 as the area, your answer is wrong. Try again.) 4 t
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