Find the area in the first quadrant bounded by a given curve and the coordinate axes by integrating with respect to y.

Vault Of Euclid

Area Under a Curve by Integrating with Respect to y

Area and arc length warmup

Find the area in the first quadrant lying under the arc from the \(y\)-axis to the first point where the curve \(x+y+y^2=2\) cuts the positive \(x\)-axis.

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What you need first

Finding intercepts of a curve
Factoring quadratic equations
Setting up definite integrals for area
Evaluating definite integrals of polynomials

What this problem tests

Tests the ability to choose the appropriate variable of integration and correctly set up and evaluate a definite integral for area.

This is a standard Calculus I problem introducing the concept of integrating with respect to y when a function is not easily expressed as y = f(x).

Area Under a Curve by Integrating with Respect to y

What you need first

What this problem tests

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