Vault Of Euclid

Evaluating a Scalar Line Integral Over a Line Segment

Multivariable calculus core

Evaluating a line integral: area under a surface over a curve. Find the area under the surface \(f(x,y) = \cos(x) + \sin(y) + 2\) over the curve \(C\), which is the segment of the line \(y = 2x + 1\) on \(-1 \leq x \leq 1,\) as shown in Figure 14.1.2.
line-integralscalar-line-integralparameterizationarea-under-surfacemultivariable-calculusdefinite-integraltrigonometric-integralscalculus-iiiarc-length-differentialvector-valued-functionsfind-areaevaluate-integral

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What this problem tests

Tests the ability to parameterize a simple curve, compute the arc length differential, and evaluate the resulting definite integral.

This problem is typical of a Calculus III or Multivariable Calculus course when introducing line integrals of scalar functions.

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