Lesson Worksheet: Area between Curves Mathematics • Higher Education

In this worksheet, we will practice applying integration to find the area bounded by the curves of two or more functions.

Q1:

The curves shown are 𝑦=1π‘₯ and 𝑦=1π‘₯. What is the area of the shaded region? Give an exact answer.

  • A1βˆ’(2)ln
  • B1+(2)ln
  • C0.3068528194
  • D0.6931471806
  • Eβˆ’0.3068528194

Q2:

Find the area of the region bounded by 𝑦=π‘₯ and 𝑦=π‘₯.

  • A12
  • B56
  • C16
  • D32
  • E43

Q3:

Find the area of the region bounded by the curves 𝑦=3π‘₯βˆ’5π‘₯ and 𝑦=βˆ’5π‘₯.

  • A2548
  • B625384
  • C125384
  • D1,37524
  • E25192

Q4:

Find the area of the region bounded by the curves 𝑦=π‘₯π‘₯ln and 𝑦=(π‘₯)π‘₯ln.

  • A5
  • B32
  • C16
  • D56
  • E13

Q5:

Find the area of the region bounded by 𝑦=√π‘₯βˆ’5 and π‘₯βˆ’3𝑦=3.

  • A556
  • B1516
  • C13
  • D916
  • E16

Q6:

Find the area of the region bounded by π‘₯=𝑦οŠͺ, 𝑦=βˆ’βˆšβˆ’2π‘₯+1, and 𝑦=0.

  • A116+5√224
  • B√28
  • Cβˆ’116+5√224
  • D√23
  • E11√260

Q7:

Find the area of the region bounded by π‘₯=𝑦 and 2π‘₯+𝑦=3.

  • A296
  • B8
  • C163
  • D283
  • E643

Q8:

Find the area of the region bounded by π‘₯=βˆ’5𝑦+1 and π‘₯=2π‘¦βˆ’5.

  • A59√4254
  • B12√427
  • C8√427
  • D80√4249
  • E10√3

Q9:

Find the area of the region bounded by 𝑦=π‘₯2,𝑦=π‘₯,βˆ’π‘₯+3𝑦=4, where π‘₯β‰₯0.

  • A2427
  • B14181
  • C12981
  • D661481
  • E5881

Q10:

Determine, to the nearest thousandth, the area of the region bounded by the curve 𝑦=√π‘₯, the line 𝑦=π‘₯βˆ’12, and the 𝑦-axis.

This lesson includes 16 additional questions and 163 additional question variations for subscribers.

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