Analysis

Problems related to calculus, limits, series, etc.

Problems in this category

We need to evaluate the definite integral: $\int_{-3}^{1} (-x^3 - x^2 + 3x + 4) \, dx$

Definite IntegralIntegrationAntiderivativePower Rule

We are given that $F(x) = \int_{\sqrt{5}}^{arcsin(cosx)} f(sint) dt = \sqrt{\frac{1-sinx}{1+sinx}}$ ...

CalculusIntegrationDifferentiationFundamental Theorem of CalculusDefinite Integrals

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

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