Evaluate the following integrals using the Fundamental Theorem of Calculus. ∫0ln⁡8exdx

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Evaluate the following integrals using the Fundamental Theorem of Calculus.  ∫0ln⁡8exdx

Froldigh · Accepted Answer

Step 1  We have to evaluate the integral using fundamental theorem of calculus:  ∫0ln⁡8exdx  We know the formula of integration through fundamental theorem of calculus,  ∫exdx=ex+C  Applying above formula for the given definite integral, we get  ∫0ln⁡(8)exdx=[ex]0ln⁡(8)  =[eln⁡(8)−e0]  Step 2  We know the property of exponential function,  eln⁡(x)=x  e0=1  So applying above property for the above result, we get  ∫0ln⁡(8)exdx=eln⁡(8)−e0  =8-1  =7  Hence, value of the definite integral is 7.

Uersfeldte · Accepted Answer

Step 1: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:  ∫abf(x)dx=F(x)∣ab=F(b)−F(a)  Step 2: In this case, f(x)=ex. Find its integral.  ex∣0ln⁡8  Step 3: Since F(x)∣ab=F(b)−F(a), expand the above into F(ln⁡8)−F(0):  eln⁡8−e0  Step 4: Simplify.  7

Evaluate the following integrals using the Fundamental Theorem of Calculus. \int_{0}^{\ln

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