# What's the best strategy to solving this Integral in 3 minutes?

• MHB
• Lorena_Santoro
In summary, an integral is a mathematical concept used to find the total value of a function over a specific interval. It is important to solve integrals quickly because they are used in many real-world applications and efficient problem-solving is crucial. The steps to solving an integral in 3 minutes involve identifying the type of integral, using appropriate integration techniques, simplifying the integral, and checking the answer. However, not all integrals can be solved in 3 minutes due to their complexity. Some tips for solving integrals quickly include regular practice, identifying patterns, simplifying the integral before integration, using technology, and double-checking the answer.
Lorena_Santoro

Please do not double post here, either.

-Dan

Separate cos^3(2x) as (cos^2(2x))cos(2x)= (1- sin^2(2x))cos(2x). Now use the substitution u= sin(2x) so that du= 2cos(2x)dx, cos(2x)dx= (1/2)du. When x= 0, u= sin(0)= 0 and when x= 4, u= sin(8). The integral becomes $$\displaystyle \frac{1}{2}\int_0^{sin(8)}(1- u^2)du=\left[u- \frac{u^3}{3}\right]_0^{sin(8)}$$$$\displaystyle = sin(8)- \frac{sin^3(8)}{3}$$.

$x = \dfrac{\pi}{4} \implies \text{ upper limit }, u= 1$

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Yes, and thank you!

## 1. What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value of a function over a given interval.

## 2. Why is solving an integral in 3 minutes important?

Solving an integral in 3 minutes is important because it allows for quick and efficient problem solving, especially in time-sensitive situations such as exams or real-life applications.

## 3. What is the best strategy for solving an integral in 3 minutes?

The best strategy for solving an integral in 3 minutes is to use techniques such as substitution, integration by parts, or trigonometric identities. It is also helpful to have a good understanding of basic integration rules and properties.

## 4. How can I improve my speed in solving integrals?

To improve speed in solving integrals, it is important to practice regularly and familiarize yourself with common integration techniques. It can also be helpful to break down the integral into smaller, more manageable parts and to use shortcuts or tricks when possible.

## 5. Are there any online resources or tools that can help with solving integrals in 3 minutes?

Yes, there are many online resources and tools available such as integral calculators, practice problems, and step-by-step tutorials. It is important to use these resources to supplement your learning and not rely on them solely for solving integrals.

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