Question

how to integrate 3t+4

Answer 1

Answer:

$t = \frac{ - 4}{3}$

Step-by-step explanation:

We can integrate this form by 3t+4 by the following ways:-

3t+4

We can now take four to the other side .

3t+4=0

3t=-4

$t = \frac{ - 4}{3}$

Answer 2

Answer: The integration of ($3t+4$) is $\frac{3t^{2} }{2}+C$

Step-by-step explanation:

Given:We have given $3t+4$.

To find:We have to integrate $3t+4$.

Explanation:

Step 1:This is an indefinite integral.that means there are many solutions represented by the constant C.

Step 2: We have given $3t+4$, on integrating with respect to t, we have,

⇒                $\int\limit {(3t+4)} \, dt = \int\limits {3t} \, dt+\int\limits {2} \, dt$

Step 3:,Since,$\int\limits {k} \, dx= kx+C$ and $\int\limits {x^{n} } \, dx = \frac{1}{n+1} x^{n+1} +C$ ,$n\neq -1$

So, we have,

⇒                $\int\limits {3t} \, dt+\int\limits {2} \, dt = \frac{3t^{2} }{2} +C$

∴ The integration of ($3t+4$) is $\frac{3t^{2} }{2}+C$

Concept:The integration is a method of addition or summing up the parts to find the whole. It is opposite process of differentiation, where we reduce the functions into small parts. This method is used to find the summation or addition under a large scale. Calculation of small addition problems is an easy task which we can do manually or by using calculators. But for very big addition problems, where the limits could reach to even up to infinity, integration methods are used. Integration and differentiation both are important parts of calculus.

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