Chapter 6.2, Problem 39E

(a)

To determine

To Find: Points of discontinuity of the integrand on the interval of integration.

Answer to Problem 39E

Function is discontinuous at $x=–1$

Explanation of Solution

Given information:

  ${{\displaystyle \int }}_{-3}^4\frac{x^2-1}{x+1}dx$

Calculation:

Function is not defined at $x=–1$ because at this value of x, function is of indeterminate form.

Hence, function is discontinuous at

  $x=–1$

(b)

To determine

To Evaluate: The given integral.

Answer to Problem 39E

The integral of the given is $-\frac{7}{2}$

Explanation of Solution

Given information:

  ${{\displaystyle \int }}_{-3}^4\frac{x^2-1}{x+1}dx$

Calculation:

For any integral function,

  ${{\displaystyle \int }}_a^{b}f(x)dx=\left(areaoftriangleabovethex-axis\right)–\left(areaoftrianglebelowthex-axis\right)$

The graph of the function:

  

So,

  ${{\displaystyle \int }}_{-3}^4\frac{x^2-1}{x+1}dx=\left(areaoftriangleabovethex-axis\right)–\left(areaoftrianglebelowthex-axis\right)$

  $\begin{array}{cc}& =\frac{1}{2}\times 3\times 3-\frac{1}{2}\times 4\times 4\\ & =\frac{9}{2}-8\\ =& \frac{9-16}{2}\\ =& -\frac{7}{2}\end{array}$