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Answer:
Four less than an unknown value E)
Quotient of a variable and four B)
Some number to the power of four A)
Four times an unknown value D)
Four more than some number C)
Step-by-step explanation:
Let's analyze each statement separately:
- Four less than an unknown value --> this means that we have to subtract 4 to an unknown value. Calling the unknown value, it means we have to write
- Quotient of a variable and four --> this means we have to divide a variable by 4. Calling the unknown variabl, it means we have to write
- Some number to the power of four --> this means that we have to write the power of a number, in the form , where m in this case is equal to 4. Calling
the unknown number, it means we have to write
- Four times an unknown value --> this means that we have to multiply an unknown value by 4. Calling our unknown values, we have to write
- Four more than some number --> this means we have to add 4 to an unknown number. Calling the unknown number, it means we have to write
Hi there!
To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine: