Help with definate integration problem

In summary, The problem involves evaluating the indefinite integral of 10^t with t between 1 and 2. The equation for this type of integral is \int(a^{x})dx = \frac{(a^x)}{ln(x)} + C, but since the lower limit is 1, plugging it in results in a division by 0. The correct answer is \frac{90}{ln(10)}, which can be obtained by switching the x and a in the equation or replacing dx with da. There is no need for a substitution rule in this problem.
  • #1
crm08
28
0

Homework Statement



[tex]\int[/tex]10[tex]^{t}[/tex]dt t = [1,2]

Homework Equations



I know that [tex]\int[/tex](a[tex]^{x}[/tex])dx = [tex]\frac{(a^x)}{ln(x)}[/tex] + C and x[tex]\neq[/tex] 1

The Attempt at a Solution



I could do this problem as indefinate, but since the restraints include a "1", I can't plug it into the the integral because it will result in a "0" being in the denominator. The answer in the back of the book shows:

[tex]\frac{90}{ln(10)}[/tex]

Should I be using a substitution rule somewhere?
 
Last edited:
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  • #2
Well, the equation in your section 2 is actually incorrect, the x and a's should be switched around ( or the dx replaced with da). That solves the problem !
 
  • #3
sorry never mind, its supposed to be the ln(a) not x
 

Related to Help with definate integration problem

What is definite integration?

Definite integration is a mathematical process used to find the exact value of the area under a curve between two given points on a graph. It involves finding the antiderivative, or the original function, of a given function and then plugging in the upper and lower limits of integration to find the area.

What are the steps for solving a definite integration problem?

The steps for solving a definite integration problem are as follows:

  1. Identify the given function and the limits of integration.
  2. Find the antiderivative of the function using integration rules or techniques.
  3. Plug in the upper and lower limits of integration into the antiderivative.
  4. Simplify the resulting expression to find the exact value of the area under the curve.

What are the common integration techniques used in definite integration?

The common integration techniques used in definite integration include substitution, integration by parts, trigonometric substitution, and partial fractions. Each of these techniques is used to solve specific types of integrals and can be chosen based on the given function.

How do I know if my answer to a definite integration problem is correct?

To check if your answer to a definite integration problem is correct, you can use the fundamental theorem of calculus. This states that the definite integral of a function f(x) between two points a and b is equal to the difference between the antiderivative of f(x) evaluated at b and a. If your answer satisfies this condition, then it is correct.

What are some real-world applications of definite integration?

Definite integration has many real-world applications, such as calculating the area under a velocity-time graph to find the displacement of an object, finding the volume of irregularly shaped objects, and determining the average value of a function. It is also used in many fields of science and engineering, including physics, economics, and computer science.

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