Mr. Orchard’s Math 142 WIR 6.1-6.3
1. Find all antiderivatives of the following functions:
(a) f
0
( x ) = 5 x
4 − 12 x + 3
(b) f
0
( x ) = 6 x 9 − 4 x 6 + 10 e x
(c) f
0
( x ) = 4 x
− 6 + 5 2
(d) f
0
( x ) =
5 x
3
(e) f
0
( x ) =
10+ x
2
5 x
Week 11

Mr. Orchard’s Math 142 WIR 6.1-6.3
Week 11
2. Find the following functions, given the derivative and a point the function passes through.
(a) f
0
( x ) = 110 x
1
3
, (0 , 0)
(b) f
0
( x ) = x
8
+
√
5 x 6 , (0 , 20)
(c) f
0
( x ) = x
4
+ 6 e x
, (0 , 7)
(d) f
0
( x ) = 15 x
2
+ 12 x + 2, (4 , 426)

Mr. Orchard’s Math 142 WIR 6.1-6.3
3. Calculate the following indefinite integrals.
(a)
R x
− 1
5
− x
1
5 dx
(b)
R
(5 + x
3
) (2 − x
5
) dx
(c)
R 35 x
7
+30 x
6 − 5
5 x 8 dx
4. Find the function F ( x ) if F
0
( x ) = x
2 x
+6 and F (5) = 0.
Week 11

Mr. Orchard’s Math 142 WIR 6.1-6.3
5. Find the most general antiderivatives of the following functions:
(a) f
0
( x ) = (9 x − 14)
12
Week 11
(b) f
0
( x ) = x 5 ( x 6 + 1) 5
(c) f
0
( x ) = x
3 x 4 +7
(d) f
0
( x ) = e 20 x
(e) f
0
( x ) = 13 x 4 e x
5

Mr. Orchard’s Math 142 WIR 6.1-6.3
6. Find f ( x ) given the following information.
(a) f
0
( x ) = e
4 x e
4 x
+5
, and f (0) = ln(6)
4
Week 11
(b) f
0
( x ) =
(ln x )
20
, and f (1) = 0 x
(c) f
0
( x ) = √ x
2
7+ x
3
, and f (1) = 10

Mr. Orchard’s Math 142 WIR 6.1-6.3
Week 11
7. The marginal revenue function for a fast food hamburger is function for the fast food chain.
− x
10000
+ 3. Find the revenue
8. A particle has a velocity function v ( t ) = 20 t
2
+ 2 t (ft/s). Approximate the distance the rocket has traveled in the first 7 seconds using n = 7 equal sub intervals.
(a) Left-Hand Sum
(b) Right-Hand Sum
(c) Upper bound
(d) Lower Bound

Mr. Orchard’s Math 142 WIR 6.1-6.3
Week 11
9. Speedometer readings for a car at 10 second intervals are given below. Estimate the distance traveled by the car using n = 6 equal sub intervals and the type of sum given.
t (s) 0 10 20 30 40 50 60 v (ft/s) 0 32.3
51.3
44 29.4
15.1
22
(a) Left-Hand Sum
(b) Right-Hand Sum
10. An object has a velocity v ( t ) =
4
+ 55 ft/s. Estimate the distance the object traveled t on the interval [2 , 12] with n = 5 equal sub intervals and the type of sum given.
(a) Left-Hand Sum
(b) Right-Hand Sum
(c) Upper Bound
(d) Lower Bound

Mr. Orchard’s Math 142 WIR
11. Find the following indefinite integrals.
(a)
R
(8 + 9 e
3 x − 2
) dx
6.1-6.3
Week 11
(b) R 1 cabin d cabin