A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
What is the integral of 1 / (1 + x2)?
Solution:
To find the value of the integral 1 / (1 + x2), we will use the substitution method of integration.
Let, I = ∫ 1 / (1 + x2) dx,
Let x = tan θ or θ = tan-1 x.
On derivating x with respect to θ, we get
⇒ dx = sec2 θ dθ
Substitute the values of x and dx in I,
⇒ I = ∫ 1 / (1 + x2) dx = ∫ [sec2 θ / (1 + tan2 θ )] dθ
Since 1 + tan2 θ = sec2 θ, on further integration we get,
⇒ ∫ sec2 θ / sec2 θ dθ
⇒ ∫ dθ = θ + c
On substituting the value of θ, we get
⇒ tan-1 x + c
Thus, the value of the integral 1 / (1 + x2) is tan-1 x + c.
What is the integral of 1 / (1 + x2)?
Summary:
The value of the integral 1 / (1 + x2) is tan-1x + c.
Math worksheets and
visual curriculum
visual curriculum