# calculus problems with answers

This calculus 1 final exam review contains 40 multiple choice and free response problems covering topics such as limits, continuity, derivatives, and integration as well as the application of ... 18.01 Final Exam Name: Please circle the number of your recitation. Your time is valuable. (a) integral (16x^3 - 15x^2 + 6) dx (b) integral (7 cos(x) + 5 sin(x)) dx, Solve the following integral: integral_0^1 (1 + x)^8 dx, Find the function F that satisfies the following differential equation and initial conditions. Here is a set of practice problems to accompany the Differentiation Formulas section of the Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University. Find the following anti-derivatives: (A) Integral of (5x^3 + 5x^2 - 10x - 6) dx, (B) Integral of -e^(-3x) dx, (C) Integral of ((9/x) - 3e^(-0.4x)) dx, Evaluate the integral: \int 4x + 9 / (x -3)(x + 4) dx. Free Math Worksheets | Free Algebra Worksheets | Video Lessons | Math Tutoring | Games | Articles | Teaching Degrees. Determine F(x) and evaluate F(x) at (1) x = 2. Do not count the area beneath the x-axis as negative. Why is stochastic calculus used in finance? (Remember to use absolute values where appropriate. Determine the function f(x) given that f' (x) = 1 + sin x and f (0) = 3. k(x) = -csc^2 \frac{6x}{5}, Find an antiderivative for the function. Find the indefinite integral: int \cos x \cot x dx. Consider the function f(t) = 10sec^{2}(t) - 4t^{2}. Evaluate the following integral. \int^4_0 \int^\sqrt{16 - x^2}_0 \int^{\sqrt{16 - x^2 - y^2}}_0 \ xy \ dzdydx. \int\frac{x-15}{x^{1}+1}dx, Evaluate the integral. Integral_{-4}^4 modulus of {2x - 1} dx. Find the curvature for \vec r(t) = \sin t \vec i + \cos t \vec j + 4 \vec k. Find the anti derivative of f(x) = 3x^5 + x - 4. Since we could look at the initial equation and see that it is an upward facing parabola, we could answer this part without actually taking the derivative but rather by knowing that a parabola’s concavity is always either upward and downward (depending on which way the parabola faces.). What does it mean when an integral is negative? The daily marginal cost to produce x widgets is found to be C'(x) = 0.000009x^2 - 0.009x + 8 (measured in dollars per unit). Use this information to find f(x). All of our calculus printables contain an answer key so you can immediately check your work. Determine which function is f(x) (the upper graph) and which function is g(x) (the lower graph) as used in the formula for the area of the region bet... Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 7 mi^2 /hr. \int_0^\frac{\pi}{4} \int_0^5 \int_0^{5 - r} rz\ dz dr d\theta, Solve the following integrals. When a certain spring is expanded 12 centimeters from its natural position and held fixed, the force necessary to hold it is 2400 dynes. Use substitution to find the antiderivatives in terms of the unspecified function f . What is the total displacement between 0 seconds and 4 seconds? In this free calculus worksheet, students must find limits of problems where the limit is approaching positive infinity or negative infinity. Evaluate the following integral : \int \frac {2x+7}{(x-1)(x+2)} dx. 16 ( tan ( x ) ) 2 sec ( x ) d x (Remember to use absolute values where appropriate. Find w(x), if w"(x) = 25e^{5x} and w'(0) = 7 while w(0) = 9. Evaluate the following integral. Get Practice AP Calculus Questions and Videos here! Each chapter begins with very elementary problems. Work the integral. What are the connections between a derivative and an integral? What is the way to find the volume in 3D space for any curve? What is the volume of the solid generated by the above rotation? Show your work. How far does the cat fall between t = 0.3 s and t = 1.6 s? \int x(x^2+1)^3\;dx A) \frac{3(x^2+1)^2}{2}+C B) \frac{x^2(x^2+1)^4}{8}+C C) \frac{(x^2+1)^4}{8}+C, Find the general indefinite integral. All other trademarks and copyrights are the property of their respective owners. csc ( 4 f ( x ) ) cot ( 4 f ( x ) ) f ( x ) d x (Recall that f ( p ) denotes the p th derivative... Find the area under the given curve.