Integral Calculus Calculator

Introduction to Integral Calculus Calculator:

The topics involved in calculus are functions, application of derivatives, limits, derivatives,  logarithm functions, trig functions and exponential functions. The two major sub divisions of calculus are differential calculus and integral calculus. In this article we shall discuss about Integral calculus calculator.  The following are the examples involved in Integral calculus calculator.

Integral Calculus Calculator Problems:


Example 1:  `int` 71ey dy

Solution: `int` 71ey dy = 71`int` ey dy

Integrating the equation, we get

`int` 71 ey dy  = 71 ey + C

Example 2:  Find `int_(-1)^1` log `((29-x)/(29+x))` dx

Solution: Let f(x) = log `((29-x)/(29+x))`

f(-x) = log`((29+x)/(29-x)) `

= log (29 + x) - log (29 - x)

= - [log(29 + x) - log(29 - x)]

= - [log`((29+x)/(29-x))` ] = -f(x)
Hence  f(-x) = -f(x), we can say that f(x) is an odd function

So, `int_(-1)^1` log`((29-x)/(29+x))`dx = 0


Example 3: Integrate the given equation 3x2+5x + 10 dx

Solution: ∫3x2+5x +10dx = ∫3x2dx +∫5x+∫10 dx

Integrating the above equation,we get 

=> 3x3+  5x2 + 10x + C
3      2     

Example 4:  Evaluate `int_0^1x e^xdx` 

Solution: Using the method of integration by parts,

As we know `int` udv = uv - `int` v du

Here u=x, du=dx, dv= exdx, v=ex

`int_0^1` x ex  dx = (x ex)10 - `int_0^1` ex  dx

= e - (ex)10

= e - (e- 1)

= 1

Example 5:  Find the integral of the given equation  23x3+4x2+2x dx

Solution: ∫3x3+4x2+2x dx 

=>∫ 3x3dx + ∫4x2 dx +∫2x dx 

Integrating the above equation

=> 3x4 +4x3 + 2x2  + c
4     3       2

Integral Calculus Calculator Practice Problems:
Problem 1: Find the integral of the given equation 4x2+2x+20 dx

Solution: 4x3 + 2x2 + 20x + c
3       2

Problem 2: Find the integral of the given equation x3+4x+50 dx

Solution: x4 + 4x2 + 50x + c
4       2

Problem 3: Find the integral of the given equation x2+2x+8 dx

Solution: x3 + 2x2 + 8x + c
3      2