Grade 12Integral Calculus

what will be the integration of e^(x^2) ? solution should be with taking care of 12^th standard student

Abhishek kumar

6 Years agoGrade 12

2 Answers

Arun

6 Years ago

2*X*e^(x^2)

The usual differentiation of e^x is e^x, this is the formula we'll use here.

As the term to be differentiated is e^(x^2)

On differentiating it would be e^(x^2) * (differentiation of x^2)

Differentiation of x^2 is 2x

So the answer is 2x*e^(x^2)

Edit: I'm sry I didn't see that.

Integration of E^(x^2) would be (e^(x^2))/2x

The same logic applies here the only difference is we divide the term rather than multiplying it.

Formula is integral of e^xis E^x

Integral of e^(x^2) would be (e^(x^2)) divided by (differentiation of x^2)

Vikas TU

6 Years ago

Dear student

ere is no elementary function that describes the antiderivative of e^x^2. We can, however, express this integral in terms of an infinite series.
e^x=1+x+x^2/2!+x^3/3!+x^4/4!+⋯= ∑ n=0to ∞ x^n/n!
ex^2= ∑n=0 to ∞ x^2n/n!
∫∑ n=0 to ∞ x^2n/n!dx = ∑n=0 to ∞ x^(2n+1) /(2n+1)n!

Hence,
∫e^x^2 dx = ∑n=0 to ∞ x^(2n+1)/(2n+1)n!