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2. Calculus II - Applications of Integrals (Practice Problems)!
3. THE CALCULUS PAGE PROBLEMS LIST.

In primary school, we learned how to find areas of shapes with straight sides e. But how do you find areas when the sides are curved? We'll find out how in:. Volume of Solid of Revolution explains how to use integration to find the volume of an object with curved sides, e. Centroid of an Area means the centre of mass. We see how to use integration to find the centroid of an area with curved sides. Moments of Inertia explains how to find the resistance of a rotating body. We use integration when the shape has curved sides. Work by a Variable Force shows how to find the work done on an object when the force is not constant.

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• Chapter Contents.

This section includes Hooke's Law for springs. You may also wish to see the Introduction to Calculus. Electric Charges have a force between them that varies depending on the amount of charge and the distance between the charges. We use integration to calculate the work done when charges are separated. Average Value of a curve can be calculated using integration. Head Injury Criterion is an application of average value and used in road safety research.

Force by Liquid Pressure varies depending on the shape of the object and its depth. We use integration to find the force.

In each case, we solve the problem by considering the simple case first. Usually this means the area or volume has straight sides. Then we extend the straight-sided case to consider curved sides. We need to use integration because we have curved sides and cannot use the simple formulas any more. The chapter begins with 1. More info: Calculus videos.

Integral Calculus

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Explanation : Before we can set up any sort of integral, we must find out where our two functions intersect, which tells of what the bounds of our region are. Example Question 3 : Applications In Physics. Explanation : Before we can begin the problem, we must remember the formula for finding the surface area of a solid formed from rotation about the x-axis: where ds is given by the following equation: So in order to set up our integral for surface area, we must first find ds, which requires us to evaluate the derivative of our function: In order to add the two terms in our radicand, we must find their common denominator.

Explanation : , so. We know. This means. Example Question 5 : Applications In Physics.

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Example Question 6 : Applications In Physics. What is the total distance travelled by the rocket during the first four seconds of its launch? Explanation : The distance traveled by an object over an interval of time is the total area under the velocity curved during the interval. Therefore, we need to evaluate the definite integral Rewriting expressions written using radical notation using fractional exponents can make applying the power rule to find the antiderivative easier.

Explanation : The work done moving an object is the intergral of force applied as a function of distance,.

Antiderivatives and Indefinite Integration, including Trig Integration - She Loves Math

Example Question 8 : Applications In Physics. Explanation : The position function is the second antiderivative of acceleration. Now integrate the velocity function to find the position function. The velocity function is. Example Question 9 : Applications In Physics.

To evaluate this, you must know the antiderivative of an exponential function. In general,.

Integral calculus

Example Question 10 : Applications In Physics. Now, we use the initial condition for the velocity function to solve for C. Finally, we write out the velocity function, with the integer replacing C:. Copyright Notice. View Calculus 2 Tutors. Mark Certified Tutor. Cornell University, Master of Science, Engineeri Nadeem Certified Tutor. University of Miami, Master of Science, Mathematics. Brytni Certified Tutor. University of Freiburg, Master of Science, Report an issue with this question If you've found an issue with this question, please let us know.

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