Evaluate the integral ∫(1 to 4) (2x + 1) dx. (2021)
Practice Questions
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Evaluate the integral ∫(1 to 4) (2x + 1) dx. (2021)
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Questions & Step-by-Step Solutions
Evaluate the integral ∫(1 to 4) (2x + 1) dx. (2021)
Step 1: Identify the integral you need to evaluate: ∫(1 to 4) (2x + 1) dx.
Step 2: Find the antiderivative of the function (2x + 1). The antiderivative is x^2 + x.
Step 3: Write down the antiderivative with the limits of integration: [x^2 + x] from 1 to 4.
Step 4: Substitute the upper limit (4) into the antiderivative: (4^2 + 4) = (16 + 4) = 20.
Step 5: Substitute the lower limit (1) into the antiderivative: (1^2 + 1) = (1 + 1) = 2.
Step 6: Subtract the result of the lower limit from the result of the upper limit: 20 - 2 = 18.
Definite Integral – The process of calculating the area under a curve defined by a function over a specific interval.
Fundamental Theorem of Calculus – This theorem connects differentiation and integration, allowing the evaluation of definite integrals using antiderivatives.
