06 - Approximating Area Under Curve - Kuta Software

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Kuta Software - Infinite Calculus
Approximating Area Under a Curve
Name___________________________________
Date________________
Period____
For each problem, approximate the area under the curve over the given interval using 4 left endpoint
rectangles.
1) y = x2
2) y = x 2 + 3; [−3, 1]
y
2 + x + 2; [−5, 3] x
y
14
14
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
x
For each problem, approximate the area under the curve over the given interval using 5 right endpoint
rectangles. You may use the provided graph to sketch the curve and rectangles.
3) y = − x2
4) y = − x2
2 + 6; [−3, 2] x
2 + x + 5; [−1, 4] x
y
y
14
12
10
8
6
4
2
14
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
−8 −6 −4 −2 2 4 6 8

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For each problem, approximate the area under the curve over the given interval using 4 inscribed
rectangles. You may use the provided graph to sketch the curve and rectangles.
5) y = −x + 5; [−7, −5]
y
14
y
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
x
6) y = 2 x ; [1, 5] 14
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8 x
For each problem, approximate the area under the curve over the given interval using 4 midpoint
rectangles. You may use the provided graph to sketch the curve and rectangles.
7) y = −x 2 + 2x + 11; [−1, 3]
8) y = x 2 − 2x + 3; [−1, 3]
y
y
14
14
12
12
10
10
8
8
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
x
−8 −6 −4 −2 2 4 6 8
x

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Kuta Software - Infinite Calculus
Approximating Area Under a Curve
Name___________________________________
Date________________
Period____
For each problem, approximate the area under the curve over the given interval using 4 left endpoint
rectangles.
1) y = x2
2) y = x 2 + 3; [−3, 1]
y
2 + x + 2; [−5, 3] x
y
14
14
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
36
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
26
x
For each problem, approximate the area under the curve over the given interval using 5 right endpoint
rectangles. You may use the provided graph to sketch the curve and rectangles.
3) y = − x2
4) y = − x2
2 + 6; [−3, 2] x
2 + x + 5; [−1, 4] x
y
y
14
12
10
8
6
4
2
14
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
−8 −6 −4 −2 2 4 6 8
25
20

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©s N2D0m1g3k jKAuGtRa1 JSSoDf3tIwsaGrjeW pLDLjCr.H 5 tANlVln Nrni2gihPtxsl rrYeEsoeNrav8emdW.W P 7M7apdbea Tw9iGtPhr SICnRfaipnMiYt0e5 3CUa9lIcSurlLuwsU.E Worksheet by Kuta Software LLC
For each problem, approximate the area under the curve over the given interval using 4 inscribed
rectangles. You may use the provided graph to sketch the curve and rectangles.
5) y = −x + 5; [−7, −5]
y
14
y
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
x
14
12
10
8
6
4
2
−8 −6 −4 −2 2 4 6 8
6) y = 2 x ; [1, 5] x
43
2 = 21.5 77
30 ≈ 2.567
For each problem, approximate the area under the curve over the given interval using 4 midpoint
rectangles. You may use the provided graph to sketch the curve and rectangles.
7) y = −x 2 + 2x + 11; [−1, 3]
8) y = x 2 − 2x + 3; [−1, 3]
y
y
14
14
12
12
10
10
8
8
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
x
−8 −6 −4 −2 2 4 6 8
x
43
13
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