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∻Solution by Steps∻ ‖ step 1 ⋮ Given the integrals $\int_{1}^{5} f(x) \, dx = 81$ and $\int_{3}^{5} f(x) \, dx = 57$, we need to find $\int_{1}^{3} f(x) \, dx$. ‖ ‖ step 2 ⋮ We can use the property of definite integrals: $\int_{a}^{b} f(x) \, dx + \int_{b}^{c} f(x) \, dx = \int_{a}^{c} f(x) \, dx$. ‖ ‖ step 3 ⋮ Applying this property, we have $\int_{1}^{5} f(x) \, dx = \int_{1}^{3} f(x) \, dx + \int_{3}^{5} f(x) \, dx$. ‖ ‖ step 4 ⋮ Substitute the given values: $81 = \int_{1}^{3} f(x) \, dx + 57$. ‖ ‖ step 5 ⋮ Solve for $\int_{1}^{3} f(x) \, dx$: $\int_{1}^{3} f(x) \, dx = 81 - 57 = 24$. ‖ ∻Answer∻ ⚹ $\int_{1}^{3} f(x) \, dx = 24$ ⚹ ∻Key Concept∻ ⚹Property of Definite Integrals⚹ ∻Explanation∻ ⚹The property of definite integrals allows us to break down or combine integrals over adjacent intervals. By using this property, we can solve for the unknown integral.⚹◊What is the integral of $f(x)$ from 1 to 5 given the equations provided in the link?⍭ Generate me a similar question◊

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