LESSON 6.14 INTEGRALS PRACTICE
1. Find the antiderivatives
a. ∫(3𝑥𝑥 4 − 7𝑥𝑥 2 + 6𝑥𝑥 − 9)𝑑𝑑𝑑𝑑
c. ∫ 4
3
√𝑥𝑥
𝑑𝑑𝑑𝑑
2
b. ∫ − 𝑥𝑥 5 𝑑𝑑𝑑𝑑
d. ∫ �
1
√𝑥𝑥
+ √𝑥𝑥� 𝑑𝑑𝑑𝑑
2. Find the area under the curve:
i.
Sketch and label the curve on the designated interval
ii.
Approximate using 5 right rectangles, 5 left rectangles, and 5 trapezoids
iii.
Compare your result to the result given by your calculator (fnInt)
2𝜋𝜋
a. ∫0 2|cos 𝑥𝑥|𝑑𝑑𝑑𝑑
2
b. ∫−1(𝑒𝑒 𝑥𝑥 − 2𝑥𝑥)𝑑𝑑𝑑𝑑
3
7
1
3√𝑥𝑥
2�𝑥𝑥 3
Answers: (1a) 𝑥𝑥 5 − 𝑥𝑥 3 + 3𝑥𝑥 2 − 9𝑥𝑥 + 𝑐𝑐 (1b) 4 + 𝑐𝑐 (1c)
+ 𝑐𝑐 (1d) 2√𝑥𝑥 +
+ 𝑐𝑐 (2a) (ii) 8.1331, 8.1331, 8.1331
2
3
5
3
2𝑥𝑥
(2b) (ii) 4.537, 3.924, 4.231 (3a) 55 (3b) 80 (3c) 9 (3d) 0.331 (3e) -1268 (3f) 424.5 (3g)4 (3h) 3/4
g. ∫0
4
4 3√𝑥𝑥
𝑑𝑑𝑑𝑑
h. ∫2
4 8
𝑥𝑥 3
e. ∫2 (3 − 4𝑥𝑥 3 ) 𝑑𝑑𝑑𝑑
6
c. ∫1
16 3
2√𝑥𝑥
f.
𝑑𝑑𝑑𝑑
∫0 (3𝑥𝑥 5 + 12𝑥𝑥 + 2) 𝑑𝑑𝑑𝑑
3
d. ∫1
𝑑𝑑𝑑𝑑
5 1
𝑥𝑥 4
a. ∫3 2𝑥𝑥 𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
b. ∫0 20 𝑑𝑑𝑑𝑑
8
4
3. Find the definite integrals below both with rules and check with your calculator.