Evaluate the integrals in Exercises 97–110.
99. ∫₀³ (√2 ...

Question

Evaluate the integrals in Exercises 97–110.

99. ∫₀³ (√2 + 1)x^(√2) dx

Accepted Answer

Welcome back everyone. Evaluate the integral from 2 to 5 of the square root of 3 x to the power of square root of 3 minus 1 dx. Let's begin this problem by rewriting the integral. We have integral from 2 to 5 of the square root of 3 multiplied by x to the power of the square root of 3 minus 1 d x. To begin with, we can factor out the constant, which is the square root of 3, and we are integrating x to the power of the square root of 3 minus 1 dx from 2 to 5. What we can do is simply apply the power rule. Let's begin by rewriting the constant square root of 3, and now let's integrate x to the power of the square root of 3 minus 1. According to the power rule, we get square x to the power of square root of 3 minus 1, the original exponent, plus 1. Divided by The original exponents square root of 3 minus 1 + 1. We are going to show that we're evaluating the result from 2 to 5 because we have a definite integral. And we can simplify, right? Because We have -1 + 1. This simply gives us 0. We can also cancel out square root of 3 divided by square root of 3 because we get 1, and this simplifies to x to the power of square root of 3 evaluated from 2 to 5. From here we want to apply the fundamental theorem of calculus part 2. We are evaluating the integral from 2 to 5, so we take 5 for x, which gives us 5 to the power of the square root of 3, and we want to subtract the value of this function at 2, which is 2 to the power of the square root of 3, and that would be our final answer 5 to the power of the square root of 3 minus 2 to the power of the square root of 3. Thank you for watching.

Evaluate the integrals in Exercises 97–110.99. ∫₀³ (√2 + 1)x^(√2) dx

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Evaluate the integrals in Exercises 97–110.
99. ∫₀³ (√2 + 1)x^(√2) dx