Calculating Areas Bounded by Curves
Read this topicExplanations 4
- We all know that integrals give areas; i.e. definite integrals given areas under curves over a particular interval. Now, let us ask a different question. If we had two curves an…
By Ahaan Rungta, Expii Team
- We already know that an integral is an area under a curve. An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. Thi…
By Maya Schwartz, Japheth Wood
- (Video) Finding Areas Between Curves by PatrickJMT Here's a video by patrickJMT where he shows you how to find any area that's between two curves. For example, suppose you had s…
By Alex Federspiel
- (Videos) Area Between Curves with Respect to yyy by PatrickJMT In these videos by patrickJMT he shows you how to find the area between curves by taking the integral with respect…
By Alex Federspiel
Problems 11
- Find the area of the region bounded by the graphs of the parabola y=x2y = x^2y=x2, the line y=xy = xy=x, and the line x=2x = 2x=2. Source: HMMT February 1998
- Let AAA be the area of the region in the first quadrant (i.e. x>0x>0x>0 and y>0y>0y>0) consisting of points above the curve y=arcsin(x)y = \arcsin(x)y=arcsin(x) and below the c…
- Find the area of the region bounded by y=4sinxy = 4\sin xy=4sinx and y=8xπy = \frac{8x}{\pi}y=π8x, where x>0x > 0x>0.
- Find the area of the region bounded by the curves y=12x2y = 12x^2y=12x2 and y=12x3y= 12x^3y=12x3.
- What is the area bounded by the following curves: the xxx-axis, the curve y=x2y = x^2y=x2, and the line tangent to that curve at x=3x=3x=3?
- Find the area of the enclosed region between the curves: y=10−2x2y=4−12x2y=10-2x^2\quad y=4-\frac12x^2y=10−2x2y=4−21x2
- Find the area of the enclosed region between the curves: x=2y2−yx+y=2x=2y^2-y\quad x+y=2x=2y2−yx+y=2
- Find the area of the enclosed region between the curves: y=x+2y=8−x2x=−1x=2y=x+2\quad y=8-x^2\quad x=-1\quad x=2y=x+2y=8−x2x=−1x=2
- Find the area between the curves. Round your answer to the nearest thousandth.
- Find the area between the curves.
- Find the area between the curves when x≥0x\ge0x≥0.