1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Stels [109]
3 years ago
13

Evaluate the integral. (Use C for the constant of integration.) cos(x) (8 + 7 sin^2(x)) dx

Mathematics
1 answer:
UNO [17]3 years ago
5 0

Answer: 8 \sin x +7(\dfrac{\sin^3x}{3})+C

Step-by-step explanation:

Consider \int \cos(x) (8+7 \sin^2(x)) \, dx

Substitute  t= sinx

then dt = cos x dx

\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C

[\int x^ndx=\dfrac{x^{n+1}}{n+1}+C]

=8 \sin x +7(\dfrac{\sin^3x}{3})+C

Hence, \int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C

You might be interested in
Hi, I just have this one problem. Please explain how you got the answer as well, thanks!
Brums [2.3K]

2/3x = 6

Multiply both sides by 3x

2 = 6.3x

2 = 18x

x = 2/18

x = 1/9

7 0
3 years ago
Read 2 more answers
S(x)= 22x-8 and f(x)= -5. What is s(x) x f(x)?
zloy xaker [14]
-110x+40
You need to use the distributive property for this problem
You multiply 22x times -5 (which is -110x) and -8 times -5 (which is 40) to get -110x+40
6 0
3 years ago
Someone, please help me lol I'm small brain
Eddi Din [679]

Answer:

Measure of EF: 1.98

Measure of AB: 6.16

Measure of HI: 12.2

Step-by-step explanation:

Trick I learned that's very helpful when solving these problems: SOH (Sine, Opposite, Hypotenuse)- CAH (Cosine, Adjacent, Hypotenuse)- TOA (Tangent, Opposite, Adjacent)

MEASURE OF EF

you're starting with angle D which is 26 degrees. You have the measure of the Hypotenuse (DF) and you're trying to find the measure of EF (the segment opposite the angle) so you would use Sine

to do the equation, i'm going to use x in place of EF. 0.44 = sin(26)

Formula: sin(angle) = (opposite)/(hypotenuse)

Equation:

0.44 = x/4.5       <----------- multiply by 4.5 to get x by itself

4.5*0.44 = x       <---------- 4.5 times 0.44

1.98= x       <----------------answer

MEASURE OF AB

trying to find hypotenuse and you already have the adjacent angle so you would use cosine. Using y in place of AB. 0.616 = sin(52)

cos(angle) = (adjacent)/(hypotenuse)

cos(52) = 10/y      <------ divide by y

y*0.616 = 10       <------------ divide by 0.616

y = 10/0.616    <----------- next you'll divide 10 by 0.616

y = 6.16    <-----------answer

MEASURE OF HI

trying to find adjacent, already have opposite so you would use tangent. tan(42) = 0.90. using z in place of HI

tan(angle) = (opposite)/(adjacent)

tan(42) = 11/z   <------------ multiply z on both sides

z*0.90 = 11  <--------- divide by 0.90 to get z by itself

z = 11/0.90    <-------- divide 11 by 0.90

z = 12.2

4 0
2 years ago
Pls help me with this :)
Firdavs [7]

Answer:

looks like school work

Step-by-step explanation:

DO IT ON YOUR OWN

6 0
3 years ago
How can you determine the equation that represents this relationship?
SOVA2 [1]
Ans: The equation that represents a proportional relationship, or a line, is y=kx, where k is the constant of proportionality. Use k=yx from either a table or a graph to find k and create the equation. Proportional relationships can be represented by tables, graphs and equations.
3 0
3 years ago
Read 2 more answers
Other questions:
  • The stopping distance of a car is directly proportional to the square of the speed of the car. If a car traveling 50 miles per h
    12·1 answer
  • Coffee cost 5$ per pound how much dose 7 pounds cost
    6·2 answers
  • Eleven twelves times two thirds
    12·2 answers
  • What is the diameter of a circle with a Circumference of 17.21? *​
    9·2 answers
  • Write an equation and solve round to the nearest hundredth when necessary 19 is what percent of 40
    6·1 answer
  • You have a box containing 6 white, 4 red, and 8 black marbles. You pick a marble and it is red. You then pick a white marble. On
    7·2 answers
  • Helpppp anyoneee plssss
    9·1 answer
  • Simply the expression by combining like terms.<br> 9x+8+3x+4=
    14·2 answers
  • How do I graph h(x) = 4|x+4| +3
    15·1 answer
  • What is the volume of the right triangular prism in cubic meters?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!