Evaluate the double integral: \iint_D e^{x^2} dA where D is the region in the first quadrant bounded by y = 0, y = 2x, and \ x = 2 . Evaluate the integral. \int (2x^5 - 3x + 4) dx \\ \int (2x^5 - 3x + 4) dx = \boxed{\space}, Simplify the expression d d x x 3 5 d p p 2, Find the indefinite integral. (b) Use the initial condition f(0) = 12 to evaluate the constant. Find f: f"(x) = -2 + 12x - 12x^2, f(0) = 4, f'(0) = 12. (b) Use f(0) = 0 to evaluate the constant. Determine if the integral converges or diverges. Introduction. \int(8 +e^x)dx = \boxed{\space} + C 3. Return to Table of Contents. \int_0^{\pi} \int_0^1 \int_0^{\sqrt{1 - z^2}} z \sin(x) dy dz dx. Expert Answer . Calculus Questions with Answers (4). Evaluate the integral \int\limits_0^4 {\int\limits_0^{\sqrt z } {\int\limits_0^\pi {\left( {{r^2}{{\cos }^2}\theta + {z^2}} \right)r \ d\theta \ dr \ dz} } } . Integral (cube root of{y^2} - 4/square root{9y}) dy, Evaluate the indefinite integral. 25 Multiple Choice: Section I, Part A 31 Multiple Choice: Section I, Part B 33 Free Response: Section II, Part A 35 Free Response: Section II, Part B 38 Answers and Rubrics (BC) Sample Questions. \int \frac{x^2}{(2x + 1)(x + 2)^2}dx \\b). … Evaluate the definite integral integral_4^5 (d / {dt} square root {3 + 5 t^4}) dt using the Fundamental Theorem of Calculus. In other words, draw a picture of the region the integral represents, and find the area using high school geometry. Evaluate the definite integral. Evaluate the iterated integral. Use C as the arbitrary constant: the integral of (1 + 8t^7)/5t dt. \int \frac{16(tan(x))^2}{sec(x)}dx, Integrate both sides of the equation using the power rule. chapter 04: elements of partial differentiation. I know that a lot of textbooks have true false questions, which I like, but I'm hoping to find a source of questions with more than two possible answers. ( 4 1 f ( x ) d x ) 1, Let f ( x ) = 4 x . Check if the answer is equivalent. Use C for the constant of integration. ), Find the most general antiderivative or indefinite integral. Express the volume V of the solid that lies under the paraboloid z = 4 - x^2 - y^2 and above the xy-plane as an iterated integral in polar coordinates. Here are a set of practice problems for the Calculus I notes. \int4x(2x^2 + 2)^2 dx = \boxed{... Find an antiderivative F ( x ) of the function f ( x ) = 1 x 8 such that F ( 1 ) = 11 . The growth rate during those 5 years is approximated by \displaystyle \frac{dh}{dt}=\frac{17.6t}{\sqrt{17.6t^... Find the arc length of the graph of the function over the indicated interval. Final Exam 2017; Final Exam 2015: questions, answers; Final Exam 2013; Final Exam 2011; Final Exam 2009; Final Exam 2007; Final Exam 2005: Part 1, Part 2; Final Exam 2003; 3359 - AP Calculus AB. Find an equation of the curve that satisfies: \dfrac{dy}{dx} = 18yx^2 and whose y-intercept is 6? Let D = {(x,y,z) in R^3 : x^2 + y^2 less than or equal to 9, 0 less than or equal to z less than or equal to 1)}. Calculus Questions with Answers (5). Evaluate the integral. Precalculus Questions and Answers Test your understanding with practice problems and step-by-step solutions. Evaluate the indefinite integral. Evaluate. If f(x) is the slope of a mountain trails at a distance of x feet from the beginning of the trail, what does the value of Integral_{100}^{500} f(x) dx means? Sketch the region enclosed by the given curves and find its area. Phone support is available Monday-Friday, 9:00AM-10:00PM ET. CSE Doubts. 7 x + 9 d x 3. x 3 ( 1 + x 4 ) 1 / 3 d, Evaluate the integral. Evaluate the following: (A) the integral of 6x^3 ln x dx, (B) the integral of 5 (sin (4x))^4 dx, (C) the integral of ((cos (7x))^2)((sin (7x))^3) dx. MATH 105 921 Solutions to Integration Exercises 9) Z x p 3 2x x2 dx Solution: Completing the square, we get 3 22x 2x = 4 (x+ 1) . for students who are taking a di erential calculus course at Simon Fraser University. Simplify the following expression: the derivative with respect to x of the integral from 11 to x^3 of dp/p^2. First evaluate \int \frac{x+3}{x^2+4x+3}dx then evaluate \int \frac{x+4}{x^2+4x+3}dx, Find the integral of the following. Find the following integral: \int \frac{1}{x^2\sqrt{x^2 + 4}} dx. Use a triple integral to calculate the volume of the enclosed solid by z = 9 - x^2, z = 0, y = 0, y = 2x. Calculus questions with detailed solutions are presented. Integral_{0}^{20} f(x) dx. Integral of (5 - e^x)/(e^(2x)) dx. Evaluate the following indefinite integral. Find the indefinite integral. \int _0^1 (1 + r)^3 \ dr, Evaluate the integral. Find the integral. An evergreen nursery usually sells a type of shrub after 5 years of growth and shaping. 8. Since 36 62, the equation becomes 6x 62 2 x, so we must have x 2 2 x which has the solution x 4 3. b) ln3 x 5 Answer. ( 2 3)x x dx 2 23 8 5 6 4. dx x xx 1 5. Integrate: the integral from 0 to pi/2 of (cos(theta))^5 d(theta). chapter 07: theory of integration Evaluate the integral. Find an antiderivative F(x) of the function f(x) = 2x^2 + 3x + 1 such that F(0) = 13. b. int_{10}^{17} (x - 9)^{-2/3} dx. Detailed solutions and explanations are also included. (b) Find the distance... Find the following integrals using partial fractions a). calculus; calculus questions and answers; Asked with an image; Question: This question hasn't been answered yet Ask an expert. Evaluate the indefinite integral. \displaystyle \int^6_... Find the particular antiderivative of the following derivative that satisfies the given condition. \int_{1}^{8} \sqrt{\frac 2x} dx. Evaluate \int_{0}^{2} f(x) dx, where f(x) = 3x^{6}, 0 less than or equal to x less than 1; and 2x^{2}, 1 less than or equal to x less than or equal to 2. 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. Now, find a different antiderivative G ( x ) of the function f ( x ) = 1 x 8 such that G ( 1... a. Sketch the solid whose volume is given by the integral and evaluate the integral: \int^\frac {\pi}{3}_0 \int^{2\pi}_0 \int^{\sec \phi}_0 p^2 \sin \phi d pd \Theta d \phi, Evaluate the following iterated integral. \int \frac {(x^3 + x^2 - 5x + 15) dx}{(x^2 + 5)(x^2 + 2x + 3)}, Compute the integral. Acceleration given by a ( t ) ) dt the line y = 3 2 x 1 x! 5 ( tan ( u + 2 using a double integral Freeman ISBN 978-1-46412-526-3, assuming that there are questions. 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