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Helga [31]
2 years ago
5

(8 pts) make an appropriate trigonometric substitution to rewrite the given integral as an integral in the angle θ with a final

answer containing no square roots. – assume all trigonometric functions are positive. – remove all square roots. – no credit will be given for using another method. – do not evaluate the integral completely. ˆ 2x √ 49 x 2 dx
Mathematics
1 answer:
svet-max [94.6K]2 years ago
5 0

The integration of 2x\sqrt{49x^{2}}dx is 2/147 (49x^{2} )^{3/2}.

Given that the function is 2x\sqrt{49x^{2}}.

We are required to find the integration of 2x\sqrt{49x^{2}}.

Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects. Therefore, in order to find the integral of a function with respect to x we have to  find the area to the X-axis from the curve.

y=\int\limit{2x\sqrt{49x^{2} } } \, dx

Put 49x^{2}=t

differentiating both sides with respect to x.

2*49x=dt/dx

2x dx=dt/49

Put the value of 2x dx=dt/49 and 49x^{2}=t

=1/49\int\limits{\sqrt{t} } \, dt

=2/ 3*49  t^{3/2}

=2/147 t^{3/2}

=2/147 (49x^{2} )^{3/2}

Hence the integration of 2x\sqrt{49x^{2}}dx is 2/147 (49x^{2} )^{3/2}.

Learn more about integration at brainly.com/question/27419605

#SPJ4

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