- #1
smadar ha
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How can I solve the following integral:
x^(0.5)*exp(x)dx
Thanks.
x^(0.5)*exp(x)dx
Thanks.
Now use integration by parts again, but this time swap your variables around so that you are integrating x-0.5 and differentiating ex.smadar ha said:I tried but it gives me another integral that I can't solve:
x^(-0.5)*exp(x)dx
Indeed it doesn't. In that case I would suggest I substitution of the form u=x0.5, followed by integration by parts. However, I will point out at this point that the integral probably cannot be written in terms of elementary functions and you will most likely have to make use of the error function.smadar ha said:if I do it I recieve:
integral(x^0.5*exp(x))=integral(x^0.5*exp(x))
and it doesn't help me...
An integral is a mathematical concept that represents the area under a curve in a graph. It is used to calculate the total value of a function over a specific interval.
The main purpose of using an integral is to calculate the total value of a function over a given interval. It is also used in various applications such as finding the area of a shape, calculating displacement in physics, and determining the probability of an event in statistics.
An integral is calculated using a process called integration, which involves finding the antiderivative of a function and evaluating it at the upper and lower limits of the given interval. This process can be done analytically or numerically using various techniques such as the fundamental theorem of calculus, substitution, and integration by parts.
A definite integral has specific limits of integration, while an indefinite integral does not. This means that a definite integral will give a numerical value, while an indefinite integral will give a function as the result. Additionally, a definite integral is used to calculate the area under a curve, while an indefinite integral is used to find the original function when its derivative is given.
Integrals are used in various fields, such as physics, engineering, economics, and statistics. Some examples of real-world applications include calculating the work done by a force, determining the volume of a solid, finding the center of mass of an object, and calculating the expected value of a random variable.