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Calculus-Integrals
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| Question | Answer |
|---|---|
| What does a definite integral find? | The area underneath a curve. |
| What is an alternative use of integrals? | Finding the length of a curve. |
| Who was credited with the first systematic technique for determining integrals? | Eudoxus. |
| Who are the founders of Calculus, in which integrals are one of the techniques that can be categorized within the field? | Isaac Newton and Liebniz. |
| Is there a power rule for integration? | No. Power rule only applies to derivatives. U substitution undoes the power rule. |
| Find the integral of 8x^7 | x^8 +C |
| Find the integral of cos(x) | sin(x) +C |
| Find the integral of 1/(25-4x^2)^(1/2) | (((sin2x/5))^(-1))/2 +C |
| Where are integrals used in the real world? | Their applications in statistics, physics(engineering), and other fields make them extremely useful. |
| Is a riemann sum equivalent to an integral? | No. Reimann sums are a cruder version of integrals, typically containing some error in their calculation. Hypothetically, with infinite rectangles, the riemann sum would be equivalent to the integral. |
| What are riemann sums? | Riemann sums are an approximation of the area underneath a curve. |
| Find the intergral of Cos (x)^4 | (12x+8sin(2x)+(sin(4x))/32 +C |
| Summarize the Mean Value Thereom for integrals. | For a continuous function there is a point that equals the average of the function from the two endpoints. |
| The intergral is the opposite of what mathamatical concept. | The derivitive. |
| True or False Intergrals can be used to find the area under curves in respect to the y-axis as well as the x-axis. | True |
| True or False Some Intergrals do not have a limit. | True |
| True or False the area under a curve will always be given by the value of an intergral | False, if the area is below the axix then it is negative and will change the value of the integral. |
| Find the intergral of 8x^3+3x^2-18x+3 | 2x^4+3x^3-9x^2+3x +C |
| What is the formula for the Volume of a curve revolved around an axis. | S (R^2)-(r^2) dr (from a to b) |
| What must you do if you are doing an improper integral? | You have to take the limit of some variable, like a,b, or c, and carry out the integration. |
| How do you tell if an integral is divergent or convergent? | When you carry out the integration and substitute variables in the integral is convergent only if terms are 0 over something or something over infinity. If there is 0 over 0 or infinity over infinity this does not meen the curve is convergent. |
| How does one take the definite integral of an equation that is non differentiable along the interval? | Break up the integral into seperate integrals. Then set up a limit where some variable approaches the value of non differentiability. |
| Who is the sugar daddy of calculus? | Bryan Zimmerman |
| What are possible tests of convergence for determining if an integral converges? | Integral test, p test, comparison test, ratio test, and nth value test. |
| Why was calculus created? | To do physics. |
| What are possible methods for doing solids of revolution? | Washer method and hollow cylinder method. |
| The derivative of the integral of a function is equal to | The original function. |
| True or False the original fuction is representative of the slop of the intergral. | True |
| What is the integral of x^(1/2) | (2(x)^(3/2))/3 +c |
| Calculus is fun | no comment |
| True or false the answear to an integral is always positive. | False it can be negative as well. |
| What is the integral of -cosx | -sinx +C |
Created by:
kmeek13
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