Question

integration of (1-cos2wt)dt will be what????
don't spam and give the answer with proper explanation....​

Answer 1

Answer:

Refer the attached picture.

Answer 2

Integration of (1-cos2wt)dt =  t - $\frac{sin2wt}{2w}$ + C, where C is the arbitrary constant of integration.

• The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated. The concept of limit is employed broadly in calculus whenever algebra and geometry are applied. Limits assist us in analysing how points on a graph behave, such as how they approach one another until their distance approaches zero.
• In mathematics, integration is a technique for combining or adding the parts to arrive at the total. It is a form of differentiation in reverse where we break down functions into their component elements. This technique is employed to determine the summation on a sizable scale. Small addition problem calculation is a simple task that can be completed manually or with the aid of a calculator. Integration techniques are employed for large addition problems, when the bounds potentially extend to infinity. Calculus includes both integration and differentiation, both of which are crucial.

Here, according to the given information, we are given that,

$\int\limits^_ \,$$(1-cos2wt)dt$

= $\int\limits 1dt-\int\limits cos2wtdt$

Now, let u = 2wt.

Then, differentiating with respect to t, we get,

$\frac{du}{dt} =2w$

Or, $dt=\frac{du}{2w}$

Then, we get,

$\int\limits^_ \,$$(1-cos2wt)dt$

= t - $\frac{sinu}{2w}$

= t - $\frac{sin2wt}{2w}$ + C, where C is the arbitrary constant of integration.

Hence, integration of (1-cos2wt)dt =  t - $\frac{sin2wt}{2w}$ + C, where C is the arbitrary constant of integration.

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