Integration

5.1 Write the equation of the tangent line to at x = 9.

5.2   Use the tangent line you just calculated to estimate

5.3   If , find y

5.4   Find

5.5   Find

5.6   Find

5.7   Find

5.8   Find

5.9   Find if , and

5.10 A car is traveling at a rate of 40 ft/sec. The brakes are applied so that the car decelerates at the constant rate of 10 ft/sec².

a)   Write an equation for velocity.
       Velocity is the derivative of acceleration

b)   Write an equation for distance (Velocity at t(0) = 0)
       Distance is the derivative of velocity

c)   How long after applying the brakes will the car stop?

d)   How far will the car travel after the brakes are applied?

5.11 Given ,

a) Estimate the area under f(x) from using a left rectangular Riemann sum consisting of 5 rectangles.

5 rectangles or five intervals so Δx =

So the Riemann sum =

b)   Evaluate

c) What feature of y = f(x) causes the left sum to be a better estimate of the area than the upper sum?
The graph’s upward concavity.

5.12 Evaluate

5.13 Evaluate

5.14 If

a)   Find

b)   Find

c)   Find