91Ó°ÊÓ

Sigma Notation What are the index of summation, the upper bound of summation, and the lower bound of summation for \(\sum_{i=3}^{8}(i-4) ?\)

Constant Multiple Rule Explain how to use the Constant Multiple Rule when finding an indefinite integral.

Definite Integral Explain how to find the area of a region using a definite integral in your own words.

Upper and Lower Sums In your own words and using appropriate figures, describe the methods of upper sums and lower sums in approximating the area of a region.

Accumulation Function Why is $$F(x)=\int_{0}^{x} f(t) d t$$ considered an accumulation function?

Recognizing Patterns In Exercises 5-8, complete the table by identifying u and du for the integral. $$\int f(g(x)] g^{\prime}(x) d x \quad u=g(x) \quad d u=g^{\prime}(x) d x$$ $$\int\left(5 x^{2}+1\right)^{2}(10 x) d x$$

Evaluating a Definite Integral as a Limit In Exercises \(5-10\) , evaluate the definite integral by the limit definition. $$\int_{-2}^{1}\left(2 x^{2}+3\right) d x$$

Evaluating a Sum In Exercises \(17-24,\) use the properties of summation and Theorem 4.2 to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result.\(\sum_{i=1}^{24} 4 i\)

In Exercises 9-36, evaluate the definite integral. Use a graphing utility to verify your result. $$\int_{1}^{8} \sqrt{\frac{2}{x}} d x$$

Evaluating a Sum In Exercises \(17-24,\) use the properties of summation and Theorem 4.2 to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result.\(\sum_{i=1}^{16}(5 i-4)\)