What is the next term in this arithmetic sequence?<br> 11, 8, 5, 2,...<br> 0-3<br> 06<br> 05

Evaluate the iterated integral 2 0 2 x sin(y2) dy dx. SOLUTION If we try to evaluate the integral as it stands, we are faced wit

nignag [31]

Answer:

Step-by-step explanation:

Given that:

$\int^2_0 \int^2_x \ sin (y^2) \ dy dx \\ \\ \text{Using backward equation; we have:} \\ \\ \int^2_0\int^2_0 sin(y^2) \ dy \ dx = \int \int_o \ sin(y^2) \ dA \\ \\ where; \\ \\ D= \Big\{ (x,y) | }0 \le x \le 2, x \le y \le 2 \Big\}$

$\text{Sketching this region; the alternative description of D is:} \\ D= \Big\{ (x,y) | }0 \le y \le 2, 0 \le x \le y \Big\}$

$\text{Now, above equation gives room for double integral in reverse order;}$

$\int^2_0 \int^2_0 \ sin (y^2) dy dx = \int \int _o \ sin (y^2) \ dA \\ \\ = \int^2_o \int^y_o \ sin (y^2) \ dx \ dy \\ \\ = \int^2_o \Big [x sin (y^2) \Big] ^{x=y}_{x=o} \ dy \\ \\= \int^2_0 ( y -0) \ sin (y^2) \ dy \\ \\ = \int^2_0 y \ sin (y^2) \ dy \\ \\ y^2 = U \\ \\ 2y \ dy = du \\ \\ = \dfrac{1}{2} \int ^2 _ 0 \ sin (U) \ du \\ \\ = - \dfrac{1}{2} \Big [cos \ U \Big]^2_o \\ \\ = - \dfrac{1}{2} \Big [cos \ (y^2) \Big]^2_o \\ \\ = - \dfrac{1}{2} cos (4) + \dfrac{1}{2} cos (0) \\ \\$

$= - \dfrac{1}{2} cos (4) + \dfrac{1}{2} (1) \\ \\ = \dfrac{1}{2}\Big [1- cos (4) \Big] \\ \\ = \mathbf{0.82682}$

5 0

2 years ago

Which equation represents a line which is perpendicular to the line 4x + 3y = - 24 ?

Scorpion4ik [409]

Answer:

C

Step-by-step explanation:

4x+3y=-24

eq. of any line perpendicular to given line is

3x-4y=a

4y=3x-a

y=3/4x -a/4

where a is an arbitrary constant.

4 0

3 years ago

On a coordinate plane, triangle R S T has points (negative 5, 6), (3, 4), and (negative 2, 2). Which expression can be used to f

ratelena [41]

How does the area of triangle RST compare to the area of triangle LMN? is 2 square units less than the The area of △ RST area of △ LMN The area of △ RST is equal to the area of △ LMN The area of △ RST is 2 square units greater than the area of △ LMN The area of △ RST is 4 square units greater than the area of △ LMN.Jun 25, 2021

7 0

2 years ago

Read 2 more answers

Simplify the expression by combining like terms 2x+8-x+10

svp [43]

Answer:

x+18

Step-by-step explanation:

Let's simplify step-by-step.

2x+8−x+10

=2x+8+−x+10

Combine Like Terms:

=2x+8+−x+10

=(2x+−x)+(8+10)

=x + 18

8 0

2 years ago

Can you add a negative and a positive when doing like term

Verdich [7]

Yes, you can add a negative and a positive when doing like terms.

5 0

3 years ago

Read 2 more answers

What is the next term in this arithmetic sequence? 11, 8, 5, 2,... 0-3 06 05