For which of the following integrands will the table method for parts produce an antiderivative?
1 answer:
Answer:
x³ sin(x)
Step-by-step explanation:
Tabular method is a special form of integration by parts. It works by taking derivatives of u and integrals of dv. You multiply diagonally, then sum the results, alternating the signs.
The important thing to note is that this will produce an antiderivative only if the derivatives of u eventually become 0. So the correct choice is x³ sin(x), because the derivatives of x³ eventually becomes 0:
d/dx (x³) = 3x²
d/dx (3x²) = 6x
d/dx (6x) = 6
d/dx (6) = 0
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Answer:
General Formulas and Concepts:
Order of Operations: BPEMDAS
Midpoint Formula:
Step-by-step explanation:
<u>Step 1: Define points</u>
J (4, 6)
K (0, -4)
<u>Step 2: Find midpoint</u>
- Substitute:
- Add/Subtract:
- Divide:
Answer:
x = 13
Step-by-step explanation:
Given that Δ NML and Δ PST are similar right triangles, we can set up the following proportional statement to establish their relationship:
Cross multiply:
8(x + 2) = 10 (x - 1)
8x + 16 = 10x - 10
Subtract 8x from both sides:
8x - 8x + 16 = 10x - 8x - 10
16 = 2x - 10
Add 10 to both sides:
16 + 10 = 2x - 10 + 10
26 = 2x
Divide both sides by 2:
13 = x
Verify whether x = 13 is the correct value:
This shows the proportional relationship between , and that ΔNML and ΔPST are indeed similar right triangles.
Therefore, the correct answer is x = 13.