Chapter 5: Problem 32
In Exercises \(27-40\) , evaluate each integral using Part 2 of the Fundamental Theorem. Support your answer with NINT if you are unsure. $$\int_{-2}^{-1} \frac{2}{x^{2}} d x$$
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
In Exercises \(19-30,\) evaluate the integral using antiderivatives, as in Example \(4 .\) $$\int _ { 1 } ^ { e } \frac { 1 } { x } d x$$
Finding Area Show that if \(k\) is a positive constant, then the area between the \(x\) -axis and one arch of the curve \(y=\sin k x\) is always $$2 / k . \quad \int_{0}^{\pi / 2} \sin k x d x=\frac{2}{k}$$
True or False The Trapezoidal Rule will underestimate \(\int_{a}^{b} f(x) d x\) if the graph of \(f\) is concave up on \([a, b] .\) Justify your answer.
Linearization Find the linearization of \(f(x)=2+\int_{0}^{x} \frac{10}{1+t} d t\) at \(x=0\)
In Exercises \(19-30,\) evaluate the integral using antiderivatives, as in Example \(4 .\) $$\int _ { 3 } ^ { 7 } 8 d x$$
What do you think about this solution?
We value your feedback to improve our textbook solutions.
