FEXAM ENGGMATH 4 INTEGRAL CALCULUS Instructions: Evaluate each of the following integral. Draw the graph of the equation with proper label/s and include what method is being used. Plane Areas: Polar Coordinates 2. Find the area enclosed by the given curve: $r^2 = a^2 (\sin \theta + \cos \theta)$ 3. Find the area enclosed by the given curve: $r = a \cos 3\theta$ 4. Find the area enclosed by the given curve: $r = a (1 - \cos \theta)$ 5. Find the area enclosed by the given curve: $r = a (3 - 2 \cos \theta)$
Added by Michael B.
Close
Step 1
Find the area enclosed by the given curve: r^2 = a^2 (sin θ + cos θ) To find the area enclosed by the curve, we need to integrate the equation with respect to θ. First, let's simplify the equation: r^2 = a^2 (sin θ + cos θ) r^2 = a^2 sin θ + a^2 cos θ Now, Show more…
Show all steps
Your feedback will help us improve your experience
Shannon K and 64 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the following general indefinite integrals. You must show your work whenever possible. (3 points each) a) ∫ a sin(bx) cos(bx) dx, where a, b ∈ ℝ, a ≠ 0, b ≠ 0. b) ∫ dx/(x² + a²). hint: x² + a² = a²(x²/a² + 1)
Adi S.
Consider the polar curves r = 2 and r = 3 + 2 sin(θ) a. Sketch the graph of these curves below. Color code the different graphs or label them well please. b. Write an integral that will represent the area contained outside the first curve (r=2) and inside the second curve (r = 3 + 2 sin(θ ). Do not evaluate the integral.
William S.
(a) ∫_C x dy - y dx, c(t) = (cos(t), sin(t)), 4π ≤ t ≤ 6π (b) ∫_C x dy + y dx, c(t) = (3 cos(πt), 2 sin(πt)), 2 ≤ t ≤ 4 (c) ∫_C yz dx + xz dy + xy dz, where c consists of straight-line segments joining (3, 0, 0) to (0, 3, 0) to (0, 0, 3) (d) ∫_C 2x^2 dx - xy dy + dz, where c is the parabola z = 4x^2, y = 0 from (-1, 0, 4) to (1, 0, 4)
Sri K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD