Find the area between the two curves and vertical lines

The video tutorial explains how to sketch graphs of functions, specifically focusing on e^x and the identity function. It guides viewers through identifying the region of interest between x=0 and x=1, and calculating the area under the curve by integrating the difference between the functions. The tutorial concludes with simplifying the result and discussing the non-calculator approach.

What is the x-intercept of the exponential function e^x?

• (1, 0)

• (0, 1)

• (1, 1)

• (0, 0)

Which function is referred to as the identity function in the video?

• f(x) = e^x

• g(x) = x

• h(x) = x^2

• j(x) = ln(x)

How do you find the area between two curves?

• Divide the area under the upper curve by the area under the lower curve

• Multiply the areas under both curves

• Subtract the area under the lower curve from the area under the upper curve

• Add the areas under both curves

What is the integral of e^x?

• 1/x + C

• ln(x) + C

• x^2/2 + C

• e^x + C

What is the simplified form of the area between e^x and x from 0 to 1?

• e + 3/2

• e - 1

• e + 1/2

• e - 3/2