Homework 4.3

1. Find the area under the given curve over the indicated interval. 

The area under the curve is ___

2. Find the area under the given curve over the indicated interval.

The area under the curve is ___ 

3.   Find the area under the given curve over the indicated interval.

$y=e^x,\left[0,5\right]$

The area is

4.  Find the area between the curve and the​ x-axis over the indicated interval.

$y=\frac{6}{x}; \left[1,10\right]$

The area under the curve is

5. Find the area under the graph of the function over the interval given.

$y=x^3; \left[1,4\right]$

The area under the curve is

6. Find the area between the curve and the​ x-axis over the indicated interval.

$y=100–x^2; \left[–10,10\right]$

The area under the curve is

7. Evaluate. Then interpret the result in terms of the area above​ and/or below the​ x-axis

${\int }_{–\frac{3}{2}}^1\left(x^3–3x\right)dx$

Interpret the result. Choose the correct answer below.

1. All of the area is above the​ x-axis.
2. The area above the x dash axis is the same as the area below it.
3. There is more area above the x dash axis than below it.
4. All of the area is below the​ x-axis. 
5. There is more area below the x dash axis than above it.

8. Evaluate

${\int }_4^9\left(\sqrt{x}–2\right) dx$

9. Evaluate

${\int }_{–4}^2{e}^t dt$

10. Evaluate

${\int }_a^{b}2e^{3t} dt$

11. Evaluate

${\int }_1^{e^4}\left(3x+\frac{3}{x}\right) dx$

12.  Evaluate

${\int }_0^6\sqrt{6x}dx$

13.   The marginal cost​ (dollars) of printing a poster when x posters have been printed is given by the following equation.

$C‘‘\left(x\right) = x^{–\frac{4}{5}}$

Find the cost of printing 82 more posters when 18 have already been printed.