Evaluate the Integral

Problem

(∫_0^45)(1/√(,t+4)*d(t))

Solution

1. Rewrite the integrand using a fractional exponent to make it easier to integrate.

(∫_0^45)((t+4)(−1/2)*d(t))

2. Apply the power rule for integration, which states that (∫_^)(un*d(u))=(u(n+1))/(n+1)

[((t+4)(1/2))/(1/2)]450

3. Simplify the expression by multiplying by the reciprocal of the denominator.

[2√(,t+4)]450

4. Substitute the upper limit of integration (t=45 and the lower limit of integration (t=0 into the expression.

2√(,45+4)−2√(,0+4)

5. Evaluate the square roots and perform the subtraction.

2√(,49)−2√(,4)

2*(7)−2*(2)

14−4

10

Final Answer

(∫_0^45)(1/√(,t+4)*d(t))=10

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