# To sketch the region bounded by the curves

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter B, Problem 54E
To determine

## To calculate: To sketch the region bounded by the curves

Expert Solution

The region bounded by the curves is sketched

### Explanation of Solution

Given information: Equation of curves are y=4x2 and x2y=2

Calculation:

Equation of curves are given as follows:

y=4x2 --------(1)

x2y=2 -------(2)

Substituting the value of y=4x2 in equation (2)

x2y=2x2(4x2)=2x8+2x2=22x2+x10=02x2+5x4x10=0x(2x+5)2(2x+10)=0(2x+5)(x2)=0x=2,52

Now, substituting the values of x=2 in equation (1)

x2y=222y=22y=0y=0

Thus, one point of intersection is (2,0)

Again, substituting the values of x=52 in equation (1)

x2y=2522y=22y=2+522y=92y=94

Thus, second point of intersection is (54,94)

Hence the area between the curves is displayed as follows:

Conclusion:

Hence, region bounded by the curves is sketched

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