Graph of cos | What is the cos(x) graph drawing?

Hello everyone dear friends. In this lesson, we will share with you what the cos graph is.

What is the graph of cos?

The plot of cos(x) is as follows:

cos graph

graph of cosx

Both graphs are graphs of cos. You can use both. Thank you so much. We wish you success in your studies.

Read More

How to find the slope of a graph? (Examples and answers)

Hello everyone, in this article, we will tell you how to find the slope of a graph and how to calculate it with examples. We wish you a good work ahead...

How to find the slope of a graph?

The slope of a line is determined by the ratio $\frac{change in y}{change in x}$ between any two points that lie on the line.

The slope is the constant rate of change of a line.

Example:

Use a graph to determine the slope of a line.

Slope of graph = -1/2

Step 1: Identify two points on the line. In this case, use (0, 2) and (2, 1).

Step 2: Calculate the vertical change from one point to the next. In this case, you must count down 1 space to move from the point (0, 2) to the point (2, 1).

Step 3: Calculate the horizontal change from one point to the next. In this case, you must count right 2 spaces to move from the point (0, 2) to the point (2, 1).

Step 4: Write the ratio showing $\frac{vertical change}{horizontal change}$ in simplest form.

In this case, the slope is represented by the ratio $\frac{-1}{2}$ , or $-\frac{1}{2}$ .

Solution: The slope is negative because the line falls from left to right.

Answer = -1/2

Practice:

Source : collegeboard.org

Read More

$\int \frac{1}{x.lnx}.dx=?$ | What is integral of 1/x.lnx?

You can reach integral of 1/x.lnx answer on this page.

What is integral of ∫1/x.lnx.dx?

Question:

$\int \frac{1}{x.lnx}.dx=?$

Solution:

Substituting $u = lnx$ and $du = \frac{1}{x}dx$, you get

$\int \frac{1}{x.lnx}.dx=\int \frac{1}{u}.du=ln|u|+C = ln|lnx| + C$

$\int \frac{1}{x.lnx}.dx=ln|lnx| + C$

Read More

Homework: In problems 1 through 20 find the area of the region R

Questions and answers of find area of region problems.

1-) R is the triangle bounded by the line y = 4 − 3x and the coordinate axes.

Answer = $\frac{8}{3}$

2-) R is the rectangle with vertices (1, 0), (−2, 0), (−2, 5) and (1, 5).

Answer = 15

3-) R is the trapezoid bounded by the lines y = x + 6 and x = 2 and the coordinate axes.

Answer = 14

4-) R is the region bounded by the curve $y = \sqrt{x}$ , the line x = 4, and the x axis.

Answer = $\frac{16}{3}$

5-) R is the region bounded by the curve $y = 4x^3$ , the line x = 2, and the x axis.

Answer = 16

6-) R is the region bounded by the curve $y = 1 − x^2$ and the x axis.

Answer = $\frac{4}{3}$

7-) R is the region bounded by the curve $y = −x^2 − 6x − 5$ and the x axis

Answer = $\frac{32}{3}$

8-) R is the region in the first quadrant bounded by the curve $y = 4 − x^2$ and the lines y = 3x and y = 0.

Answer = $\frac{19}{6}$

9-) R is the region bounded by the curve $y = \sqrt{x}$ and the lines y = 2 − x and y = 0.

Answer = $\frac{7}{6}$

10-) R is the region in the first quadrant that lies under the curve $y = \frac{16}{x}$ and that is bounded by this curve and the lines y = x, y = 0, and x = 8.

Answer = 8(1+ln4)

11-) R is the region bounded by the curve $y = x^2−2x$ and the x axis. (Hint: Reflect the region across the x axis and integrate the corresponding function.)

Answer = $\frac{4}{3}$

12-) R is the region bounded by the curves $y = x^2 + 3$ and $y = 1 − x^2$ between x = −2 and x = 1.

Answer = 12

13-) R is the region bounded by the curve $y = e^x$ and the lines y = 1 and x = 1.

Answer = e-2

14-) R is the region bounded by the curve $y = x^2$ and the line y = x.

Answer = $\frac{1}{6}$

15-) R is the region bounded by the curve $y = x^2$ and the line y = 4.

Answer = $\frac{32}{3}$

16-) R is the region bounded by the curves $y = x^3 − 6x^2$ and $y = −x^2$.

Answer = $\frac{625}{12}$

17-) R is the region bounded by the line y = x and the curve $y = x^3$.

Answer = $\frac{1}{2}$

18-) R is the region in the first quadrant bounded by the curve $y = x^2 + 2$ and the lines y = 11 − 8x and y = 11.

Answer = $\frac{40}{3}$

19-) R is the region bounded by the curves $y = x^2 − 3x + 1$ and $y = −x^2 + 2x + 2$.

Answer = $\frac{11}{8}\sqrt{33}$

20-) R is the region bounded by the curves $y = x^3 − x$ and $y = −x^2 + x$.

Answer = $\frac{37}{12}$

Read More

What is integral of x^3/4 | $\int x^{\frac{3}{4}}.dx=?$

You can reach integral of x^3/4 answer on this page.

What is integral of ∫x^3/4.dx?

integral of x^3/4

$\int x^{\frac{3}{4}}.dx=\frac{4}{7}.x^{\frac{7}{4}}+C$

Read More

$x.e^{-x}$ integral | What is integral of x.e^-x? | $\int x.e^{-x}.dx=?$

You can reach integral of x.e^-x answer on this page.

What is integral of ∫x.e^-x.dx?

x.e^-x integral

$\int x.e^{-x}.dx=-(x+1).e^{-x}+C$

Read More

$x.lnx^2$ integral | What is integral of x.lnx^2? | $\int x.lnx^2.dx=?$

You can reach integral of x.lnx^2 answer on this page.

What is integral of ∫x.lnx^2.dx?

Solution. In this case, the factor $X$ is easy to integrate, while the factor ln $x^2$ is simplified by differentiation. This suggests that you try integration by parts with:

$\int x.lnx^2.dx=\frac{1}{2}.x^2(lnx^2-1)+C$

Read More