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Evaluate the integral
Evaluate the integral
For each indefinite integral, evaluate the integral. For each
definite
integral, evaluate the integral or show that it is
divergent.
******Please try not to use U-sub, I do not understand how the
online step by step calculators solve using
4. a and b
8+2x2 r(arctan(x))dx
8+2x2 r(arctan(x))dx
Evaluate the integral
Evaluate the integral
Problem 6. ( 25 points) Let \(a, b\) be positive constants with \(a<b\). Evaluate the integral$$ \int_{0}^{1} \frac{x^{b}-x^{a}}{\ln x} d x $$by converting the integral into an iterated double integral and evaluating the iterated integral by changing the order of integration.
Evaluate the indefinite integral as an infinite series.
A)
Evaluate the indefinite integral as an infinite series. 5 ex - 1/8x dx
3. [10 pts.] Evaluate the tripe integral \(\iiint_{E} \sqrt{x^{2}+y^{2}+z^{2}} d V\) where \(E\) is the solid ballbounded by the sphere \(x^{2}+y^{2}+z^{2}=2 z\)
Evaluate the surface integral \(\iint_{S} F \cdot d \mathbf{S}\) for the given vector field \(\mathbf{F}\) and the oriented surface \(S\). In other words, find the flux of \(F\) across 5 . For closed surfaces, use the positive (outward) orientation.$$ \mathbf{F}(x, y, z)=x \mathbf{i}+3 y \mathbf{j}+2 z \mathbf{k} $$\(S\) is the cube with vertices \((\pm 1, \pm 1, \pm 1)\)
Problem 5. (25 points) Use cylindrical coordinates to evaluate \(\iiint_{D} 1 d V\), where \(D\) is the solid region that lies within the cylinder \(x^{2}+y^{2}=1\), above the plane \(z=1\), and below the cone \(z^{2}=4 x^{2}+4 y^{2}\)
evaluate the indefinite integral
Evaluate the Integral
Evaluate the integral TT " 9 - sin 10x dx 10