CALCULUS I
Worksheet #46
1.
2

Suppose f and g are continuous functions and that:
5
f ( x)dx  4 and
1
1
5
Find:
a)
2.
Suppose f and h are continuous functions and that:  f ( x)dx  1 and
1
9
a)  2 f ( x)dx
Find:
9
3.
7
b)  [2 f ( x)  h( x)]dx
c)
7
1
1
d)
 f ( x)dx
9
 f ( x)dx  5
7
Suppose f is continuous on [0,4] and that:
 f ( x)dx  3
0
9
and  h( x)dx  4
7
7
d)  [ f ( x)  h( x)]dx
7
9
3
 f ( x)dx
5
1
7
 g ( x)dx  8
5
c)  [4 f ( x)  2 g ( x)]dx
5
1
2
5
b) 4 f ( x)dx
 f ( x)dx

5
f ( x)dx  6 and
4
and
 f ( x)dx  7
0
4
 f ( x)dx
Find
3
4.
2
Suppose f and g are continuous functions and that:

5
f ( x)dx  3 and
1
5
Find:
 f ( x)dx
a)
1
5.
6.
7.
x

1
b) 4 f ( x)dx
5

5
f ( x)dx  7 and
2
 g ( x)dx  9
1
5
c)  [4 f ( x)  2 g ( x)]dx
1
4
dx 
1
2
5
1  x2
dx 
4
Find
 (i
2
 1) 
From Algebra 2: This notation means "find the sum"
i 1
8.
Find the approximate area for four equal intervals by a) left-endpoint rectangles, b) right-endpoint
rectangles, c) midpoint rectangles, d) trapezoid rule, and e) the exact area by integral.
In parts a, b, c and d find the answer correct to 3 places past the decimal point.
4

xdx
0
9.
m3
Sand is falling into a conical pile at the rate of 10 sec such that the height of the pile is always half the
diameter of the base of the pile. Find the rate at which the height of the pile is changing when the pile is 5
1


m. high. V  r 2 h 
3


10. Find the average value of the function f(x) = x sin x on the closed interval [1,π]. Use your calculator to
find the answer - round to 3 decimal places.
11. Find the area between the line y = 9 and the parabola y = x2.
12. Determine whether the conditions for Rolle's Theorem are met for f(x) = x2 – 8x on [0,8]. If they are, then
find c; if not, tell why the conditions are not met.
CALCULUS I
Worksheet #46
13. Find the value of k such that the following function is continuous for all real numbers.
for x 2
f(x) = 3kx 5
4x 5k
for x2
e
14.
Use your calculator - round your answer to 3 decimal places:  x 2 ln xdx

1
Answers:
1) 2; 8; -8; 0
6) 5sin 1 x  C
11) 36
2) -8; 6; -5; 0 3) 4
4) 4; 16; -2 5) 4 tan 1 x  C
7) 26
8) 4.15; 6.15; 5.38;
10) 1.326
2
9)
m/s
5.145; 16/3
5
12) 4
14) 4.575
13
13)
11