Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We are given the following information: $F(x) = \int_{\sqrt{2}}^{\arcsin(\cos x)} f(\sin t) dt = \sq...

CalculusDefinite IntegralsFunctionsEvaluation of Integrals

We need to find the mass $m$ and center of mass $(\bar{x}, \bar{y})$ of the lamina bounded by the cu...

CalculusDouble IntegralsCenter of MassIntegration by PartsLamina

The problem asks us to find the mass $m$ and the center of mass $(\bar{x}, \bar{y})$ of the lamina b...

Multiple IntegralsCenter of MassDouble IntegralsDensity FunctionLamina

The problem asks to find the mass $m$ and the center of mass $(\bar{x}, \bar{y})$ of a lamina bounde...

Multivariable CalculusDouble IntegralsCenter of MassLaminaDensity Function

The problem asks us to find the value(s) of $a$ such that the function $f(x) = x^3 + ax^2 + 3x - 4$ ...

CalculusDerivativesIncreasing FunctionQuadratic InequalitiesDiscriminant

The problem is to evaluate the double integral $\int_0^{\pi/2} [\frac{1}{2} \int_4^0 \sqrt{u} \, du ...

CalculusIntegrationDouble IntegralDefinite Integral

We need to evaluate the double integral $\iint_S y \, dA$, where $S$ is the region in the first quad...

Double IntegralsPolar CoordinatesMultivariable Calculus

We need to evaluate the double integral $\iint_S \sqrt{4-x^2-y^2} \, dA$, where $S$ is the first qua...

Multiple IntegralsDouble IntegralsPolar CoordinatesIntegrationCalculus

The problem asks to reverse the order of integration of the iterated integral $\int_0^1 \int_{-y}^y ...

Iterated IntegralsChange of Order of IntegrationCalculus of Several Variables

We are given the iterated integral $\int_{0}^{1} \int_{x^2}^{x^{1/4}} f(x, y) dy dx$. We need to cha...

Iterated IntegralsChange of Integration OrderCalculus

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