Evaluate the Integral

Problem

(∫_0^3)(35*et*d(t))

Solution

1. Identify the constant and the function to be integrated. The constant 35 can be moved outside the integral.

(∫_0^3)(35*et*d(t))=35*(∫_0^3)(et*d(t))

2. Apply the rule for the integral of the natural exponential function, which is (∫_^)(et*d(t))=et

35*[et]30

3. Evaluate the definite integral by substituting the upper limit 3 and the lower limit 0 into the expression.

35*(e3−e0)

4. Simplify the expression using the property that any non-zero number raised to the power of 0 is 1

35*(e3−1)

5. Distribute the constant to find the final exact value.

35*e3−35

Final Answer

(∫_0^3)(35*et*d(t))=35*e3−35

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