To state: The rule for
Explanation of Solution
Explanation to state the rule for integration by parts:
The rule that corresponds to the Product Rule for differentiation is called as the integration by parts.
The product Rule states that if f and g are differentiable functions, then
Integrate both sides of the Equation for indefinite integrals.
Consider
Differentiate both sides of the above Equations.
Substitute u for
Therefore, the rule for integration by parts is
Example to use the rule for integration by parts:
Consider the integral function
Consider
Differentiate both sides of the Equation.
Consider
Integrate both sides of the Equation.
Substitute x for u, dx for du,
Therefore, the value of the integral function
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Chapter 7 Solutions
Single Variable Calculus: Early Transcendentals
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