We are integrating f(x) = 9cos(9x) + 3x²:
a) Apply the sum rule
b) Calculate each antiderivative
<u>First integral</u>
1. Take out the constant
2. Apply u-substitution, where u is 9x
3. Take out the constant (again)
4. Take the common integral of cos, which is sin
5. Substitute the original function back in for u and simplify
6. Always remember to add an arbitrary constant, C, at the end
<u>Second integral</u>
1. Take out the constant
2. Apply the power rule, , where <em>a</em> is your exponent
⇒
3. Add the arbitrary constant
c) Add the integrals
sin(9x) + C + x³ + C = sin(9x) + x³ + C
Notice the two arbitrary constants. Since we do not know what either constant is, we can combine them into one arbitrary constant.
<h3>
Answer:</h3>
F(x) = sin(9x) + x³ + C
Answer:
Step-by-step explanation:
3y + 1 - 2y = -3 -3y
4y = -4
y = -1
Answer:
what
Step-by-step explanation:
We can find h by calculating the area S of the parallelogram in two ways. We can write:
. On the other hand,
. Then:
So if in 1/4 of an hour 75 gallons are pumped you would multiply 75 by four which will give you 300. This means 300 gallons are pumped in an hour