Find the Integral Using an Appropriate Trigonometric Substitution $$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 36 } } d x$$

question 101

Multiple Choice

Find the integral using an appropriate trigonometric substitution.
$$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 36 } } d x$$ Select the correct answer.

• A) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 36 \right) ^ { 3 / 2 } \sqrt { x ^ { 2 } + 36 } + C\)
• B) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 72 \right) \sqrt { x ^ { 2 } + 36 } + C\)
• C) \(\frac { 1 } { 3 } \left( x ^ { 2 } - 72 \right) \sqrt { x ^ { 2 } + 36 } + C\)
• D) \(\frac { 1 } { 3 } \left( x ^ { 2 } - 36 \right) ^ { 3 / 2 } \sqrt { x ^ { 2 } + 36 } + C\)

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Definitions:

Present Value Index

A calculation that compares the present value of project cash inflows with the initial investment, used in capital budgeting to evaluate profitability.

Compound Interest

The process of computing interest by including both the primary sum borrowed or deposited and the interest that has previously accumulated over time.

Estimated Cost

A prediction or approximation of the cost of goods or services, based on current and past information, before the actual expense is known.

Net Present Value

A method used in capital budgeting to determine the profitability of an investment by calculating the sum of its present values of all expected future cash flows.