4. Follow the steps below to compute the integral ∫ ??/(1 − 4?^2)^3/2 a) Using the substitution 2? = sin(?), compute the differential ?? and convert (1 − 4?^2)^3/2 to a simplified equation of ?. b) Use what you found in (a) to rewrite the integral. Then simplify the integrand and integrate with respect to ?. Your answer here will be in the variable ?. c) Draw a right triangle in the space below and label one of the acute angles as ?. Use the equation 2? = sin(?) with right triangle trigonometry (SOH CAH TOA) to label two of the three sides of the triangle. Then, use the Pythagorean Theorem to find and label the remaining side length of the triangle.
4. Follow the steps below to compute the integral ∫ ??/(1 − 4?^2)^3/2 a) Using the substitution 2? = sin(?), compute the differential ?? and convert (1 − 4?^2)^3/2 to a simplified equation of ?. b) Use what you found in (a) to rewrite the integral. Then simplify the integrand and integrate with respect to ?. Your answer here will be in the variable ?. c) Draw a right triangle in the space below and label one of the acute angles as ?. Use the equation 2? = sin(?) with right triangle trigonometry (SOH CAH TOA) to label two of the three sides of the triangle. Then, use the Pythagorean Theorem to find and label the remaining side length of the triangle.
4. Follow the steps below to compute the integral ∫ ??/(1 − 4?^2)^3/2 a) Using the substitution 2? = sin(?), compute the differential ?? and convert (1 − 4?^2)^3/2 to a simplified equation of ?. b) Use what you found in (a) to rewrite the integral. Then simplify the integrand and integrate with respect to ?. Your answer here will be in the variable ?. c) Draw a right triangle in the space below and label one of the acute angles as ?. Use the equation 2? = sin(?) with right triangle trigonometry (SOH CAH TOA) to label two of the three sides of the triangle. Then, use the Pythagorean Theorem to find and label the remaining side length of the triangle.
4. Follow the steps below to compute the integral ∫ ??/(1 − 4?^2)^3/2 a) Using the substitution 2? = sin(?), compute the differential ?? and convert (1 − 4?^2)^3/2 to a simplified equation of ?. b) Use what you found in (a) to rewrite the integral. Then simplify the integrand and integrate with respect to ?. Your answer here will be in the variable ?. c) Draw a right triangle in the space below and label one of the acute angles as ?. Use the equation 2? = sin(?) with right triangle trigonometry (SOH CAH TOA) to label two of the three sides of the triangle. Then, use the Pythagorean Theorem to find and label the remaining side length of the triangle.
Transcribed Image Text:4. Follow the steps below to compute the integral
dx
Ja- 4x²)3/2
a) Using the substitution 2x = sin(0), compute the differential dx and convert (1 – 4x²)3/2 to a
simplified equation of 0.
b) Use what you found in (a) to rewrite the integral. Then simplify the integrand and integrate
with respect to 8. Your answer here will be in the variable 6.
c) Drawa right triangle in the space below and label one of the acute angles as 0. Use the
equation 2x = sin(0) with right triangle trigonometry (SOH CAH TOA) to label two of the three
sides of the triangle. Then, use the Pythagorean Theorem to find and label the remaining side
length of the triangle.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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