Question

(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

Answer 1

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 49$x^{2}$=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 49$x^{2}$=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