2022-04-23
Find the area of the region bounded by the graphs of the given equations. 𝑦 = 𝑥 2 − 3𝑥 + 3, 𝑦 = −𝑥 + 3
nick1337
Expert2022-07-31Added 777 answers
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Solve by substitution to find the intersection between the curves.
Eliminate the equal sides of each equation and combine.
Solve for .
Evaluate when .
Evaluate when .
The solution to the system is the complete set of ordered pairs that are valid solutions.
The area of the region between the curves is defined as the integral of the upper curve minus the integral of the lower curve over each region. The regions are determined by the intersection points of the curves. This can be done algebraically or graphically.
Integrate to find the area between and .
Combine the integrals into a single integral.
Simplify each term.
Simplify by adding terms.
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Combine and .
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Simplify the answer.
Combine and .
Substitute and simplify.
Evaluate at and at .
Evaluate at and at .
Simplify.
Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
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