How to calculate the square integral of E?

If you can't get the product of elementary functions, you can get the method of double integral. This problem is mentioned in general mathematics books,
[∫exp(x^2)dx]^2
=∫exp(y^2)dy∫exp(x^2)dx
=∫∫exp(x^2+y^2)dxdy
See the expression of a circle, replace it with polar coordinates
=∫∫rexp(r^2)drdθ
Suppose the radius of the circle is r
=2π[(1/2)exp(r^2)] =π[exp(a^2)-1]
So ∫ exp (x ^ 2) DX = π [exp (a ^ 2) - 1])

The known angle α (0

45 degrees or 225 degrees

RELATED INFORMATIONS

1. In the triangle ABC, the three angles satisfy 2A = B + C, and the maximum and minimum edges are the two roots of the equation 3x ＾ 2-27 + 32 = 0, respectively Then a = It's 27x, not 27
2. Given that the three sides of triangle ABC are m, N, √ m ^ 2 + Mn + n ^ 2, find the maximum angle of triangle ABC
3. In RT △ ABC, the angle c = 90 ° and if Tana = 3, then the value of SINB is
4. What is the probability that the sum of any two real numbers in the closed interval [- 1,1] is not greater than 1
5. It is known that 2 + AI and B + I are two quadratic equations with real coefficients x times x + PX and q = 0, then the values of P and Q are?
6. When solving a quadratic equation of one variable, if a misprints the constant term and gets roots of - 2 and - 3, and B misprints the primary term and gets roots of 6 and - 1, then the correct equation is
7. It is known that the solution sets of the equations X & sup2; - Px + 15 = 0 and X & sup2; - 5x + q = 0 are m and s, and m ∩ s = {3}. Find m ∪ s
8. If the solution set of inequality (M + 1) x > m + 1 about X is X
9. If the equation AX2 + 2x + 1 = 0 has and only has one negative root, then the value range of a is______ ．
10. When x = 2, the value of PX & sup3; + QX + 1 is 2005 How much does this formula equal
11. If a is an acute angle and Tan (a + 10 °) = 1, then a=
12. Given that the acute angle A. B satisfies Tan (a + b) = 2tana, the maximum value of Tana is?
13. If a B is an acute angle and (1-tan a) (1-tan b) = 2, then a + B=
14. Two sharp angles a and B are known simultaneously: (1) a + 2B = 120 (2) Tan (A / 2) * Tan B = 2-radical 3. Find the value of a and B
15. Prove that f and G are inverse functions? F (x) = x + 7, G (x) = X-7
16. Why is x > = 0 when finding the inverse function of hyperbolic cosine function y = CHX?
17. The process of solving a hyperbolic sine to inverse hyperbolic sine Please master help me analyze the following formula is how to come out to the detailed process, hyperbolic sine inverse function y = sh x, x = sh y How can I find the line x = (e ^ y-e ^ - y) / 2, Let u = e ^ y, then the above formula has u ^ 2-2xu-1 = 0, which is the same as above, His root is u = x + - so is the line x ^ 2 + 1 under the root Easy to understand is the best
18. If we know that △ ABC is an obtuse triangle and the lengths of its three sides are continuous positive integers, then the cosine of its maximum internal angle is______ ．
19. The derivative of e to the (x + 3) power RT
20. If SiNx is greater than or equal to - 1 / 2, what is the value range of X