Calculating Area Under a Piecewise Function

The video tutorial explains how to determine the area under a piecewise-defined function on a closed interval from 1 to 6. The function is divided into two parts: a red line from 1 to 4 and a blue line from 4 to 6. The tutorial demonstrates using definite integrals to calculate the area, requiring two separate integrals for each segment. The antiderivatives are evaluated at specific points to find the total area of the shaded region. The video concludes by noting that the regions could also be calculated using trapezoid area formulas, but calculus techniques are preferred.

What is the interval on which we need to find the area under the piecewise function?

• 0 to 5

• 3 to 8

• 1 to 6

• 2 to 7

Which line bounds the area from x = 1 to x = 4?

• Green line

• Red line

• Blue line

• Yellow line

What is the function used for the interval from 1 to 4?

• x^2 + 3

• 4x - 1

• 2x + 1

• 3x + 2

What is the function used for the interval from 4 to 6?

• 10 - x

• 15 - x

• 12 - x

• 13 - x

What is the antiderivative of 2x?

• x^2 + x

• x^2 - x

• x^2

• 2x^2

What is the antiderivative of 13 - x?

• 12x - x^2/2

• 14x - x^2/2

• 13x + x^2/2

• 13x - x^2/2

What is the total area of the green shaded region?

• 32 square units

• 36 square units

• 34 square units

• 30 square units

What shape are the regions on the left and right of the shaded area?

• Circles

• Rectangles

• Triangles

• Trapezoids

What alternative method could have been used to find the area?

• Using rectangles

• Using triangles

• Using trapezoid area formula

• Using circles

What is the purpose of using calculus techniques in this problem?

• To find the area

• To find the perimeter

• To find the length

• To find the volume