The Definite Integral (6.1 and 6.2)

The Definite Integral

​

​Chapter 6

Estimating with
Finite Sums

​

​ 6.1

​Rectangular Approximation Method (RAM)

​LRAM

​MRAM

RRAM

Definite Integrals

​ 6.2

​Riemann Sums

5 Ideas to solve Infinite Integrals

​​1^st Idea

Multiple Choice

Evaluate.

• 15

• 1

• -9

Multiple Choice

Evaluate.

• 15

• 1

• -80

Multiple Choice

Evaluate.

• 15

• 4

• -80

​​The Integral is the area under the curve.
In 2^nd Idea we use the meaning so we use the area rules not the integrals rule.

​​2^nd Idea

Multiple Choice

$$15.\ \ \ \int_{-3}^3\ \sqrt[]{9-x^2}dx$$

• $$\frac{9\pi}{2}$$

• $$4\pi$$

• $$2\pi$$

Multiple Choice

$$16.\ \ \ \int_{-4}^0\ \sqrt[]{16-x^2}dx$$

• $$\frac{9\pi}{2}$$

• $$4\pi$$

• $$2\pi$$

Multiple Choice

$$Example2.\ \ \ \int_{-2}^2\ \sqrt[]{4-x^2}dx$$

• $$\frac{9\pi}{2}$$

• $$4\pi$$

• $$2\pi$$

​​3^rd Idea

Multiple Choice

$$47.\ \ \ \int_{-1}^1\ x^3dx$$

• 21

• 0

• 13/4

Multiple Choice

$$48.\ \ \ \int_{-1}^1\ x^3+3\ dx$$

• 21

• 0

• 13/4

Multiple Choice

$$13.\ \ \ \int_{-2}^4\ \frac{x^{ }}{2}+3\ dx$$

• 21

• 0

• 13/4

Multiple Choice

$$14.\ \ \ \int_{\frac{1}{2}}^{\frac{3}{2}}\ -2x+4\ \ dx$$

• 2

• 0

• 13/4

​​4^th Idea The Integral of absolute value .

Multiple Choice

$$17.\ \ \ \int_{-2}^1\ \left|x\right|\ dx$$

• 1

• 0

• 5/2

Multiple Choice

$$37.\ \ \ \int_{-2}^3\ \frac{x}{\left|x\right|}\ dx$$

• 1

• 0

• 5/2

​​5^th Idea we simplfy first then
we integrate.

Multiple Choice

$$39.\ \ \ \int_{-3}^4\ \frac{x^2-1}{x+1}\ dx$$

• 1

• 0

• -7/2

Multiple Choice

$$\ \ \ \int_0^3\ \frac{x^2-4}{x-2}\ dx$$

• 1

• 21/2

• -7/2