Solve Calculus Help Integrals

Introduction for solve calculus help integrals:

Calculus is divisions in mathematics. It contains limits, functions, derivatives, integrals, and infinite series. Calculus is divided into two major parts, differential and integral calculus, which are associated by the basic theorem of calculus. Calculus is the learning of vary, in the equal way that geometry is the learning of shape and algebra is the learning of procedure and their application to solving equations.A math tutorial is one technique of shifting knowledge and may be used as a piece of learning. More interactive and detailed than a book; a tutorial look for to tutor by example and provide the information to complete a certain task.I like to share this Triple Integrals with you all through my article.

3 important topics involved in Calculus are,

Limits

Derivatives

Integrals

Solve Calculus Help Integrals - Examples

Solve calculus help integrals - Example 1:

Integrate the given equation with respect to x, we get

`int ` x7 dx = `(x^7 +1)/(7 + 1) ` + c

= `(x^8)/8 ` + c

Answer:

The final answer is  ` (x^8)/8` + C

Solve calculus help integrals - Example 2:

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Evaluate:

`int` e(5x+3) dx

Solution:

Put (5x+3) =t so that 5 dx = dt or dx =`1/5` dt.

= `int` e(5x+3) dx =`1/5` et + C

= `1/5` e (5x+3) + C

Solve calculus help integrals - Example 3:

Integrate the given function int 2 sin 4x dx

Solution:

Integrate the given function with respect to x, we get

`int` 2 sin 4x dx = 2 `int` sin 4x dx

= 2 `xx`  - cos `(4x)/4`

= - cos `(4x)/4`

Answer:

The final answer is - cos` (4x)/4`

Solve Calculus Help Integrals - more Examples:

Solve calculus help integrals - Example 1:

Integrate int arcsin 2x dx

Solution:

U = arcsin 2x and du = dx = 1 dx

du =` 1/sqrt (1-(2x)^2) 2 dx = 2/sqrt(1-4x^2) dx ` and  v=x..

Therefore,

int arcsin 2xdx = x arcsin 2x – `int x 2/(sqrt(1-4x^2))` dx  = x arcsin 2x – 2` int x/(sqrt(1-4x^2))` dx.

Now apply u-substitution.

Let     U = 1-4x2

du = -6x dx,

`(-1/6)` du = x dx.

`int `  arcsin 2x dx = x arcsin 2x – 2` int` `x/sqrt(1-4x^2)` dx

= x arcsin 2x-2 `int 1/(sqrt(1-4x^2))` x dx

= x arcsin 2x-2 `int 1/sqrt(u) (-1/6)` du

= x arcsin 2x + `(1/3) int 1/sqrt(u)` du

= x arcsin 2x +` (1/3) int ` u-1/2 du

= x arcsin 2x+ `(1/3) (u^(1/2))/(1/2)` + C

= x arcsin 2x + `1/3(1-4x2)^(1/2)` + C

= x arcsin 2x +` (1/3) sqrt(1-4x^2)` + C.

Solve calculus help integrals - Example 2:

Evaluate:

1) `int` cos 2x dx

2) `int` e(4x+3) dx

Solutions:

1)    Put 2x =t so that 2 dx    = dt or dx =`1/2` dt.

= `int` cos 2x dx =`1/2` sin t + C

= `1/2` sin 2x + C

2)    Put (4x+3) =t so that 5 dx = dt or dx =`1/4` dt.

= `int` e(4x+3) dx =`1/4` et + C

= `1/4` e (4x+3) + C