Asked by Ozair
Evaluate the following indefinite integrals.
i.du/u²
ii. 6dv/v⅝
i.du/u²
ii. 6dv/v⅝
Answers
Answered by
Bosnian
In both case apply the Power Rule:
∫ xⁿ dx = ( x ⁿ ⁺ ¹ ) / ( n +1 ) + C
∫ du / u²
∫ du / u² = ∫ u ⁻² ∙ du= ( u ⁻² ⁺ ¹ ) / ( - 2 +1 ) + C =
u ⁻¹ / ( - 1 ) + C = - 1 / u + C
∫ 6 dv / v⅝ = 6 ∫ dv / v⅝ = 6 ∫ v ⁻ ⅝ dv = 6 v ⁻ ⅝ ⁺ ¹ / ( - 5 / 8 + 1 ) + C =
6 v ⅜ / ( 3 / 8 ) + C = 6 ∙ 8 ∙ v ⅜ / 3 + C = 3 ∙ 2 ∙ 8 ∙ v ⅜ / 3 + C =
2 ∙ 8 ∙ v ⅜ + C = 16 ∙ v ⅜ + C
∫ xⁿ dx = ( x ⁿ ⁺ ¹ ) / ( n +1 ) + C
∫ du / u²
∫ du / u² = ∫ u ⁻² ∙ du= ( u ⁻² ⁺ ¹ ) / ( - 2 +1 ) + C =
u ⁻¹ / ( - 1 ) + C = - 1 / u + C
∫ 6 dv / v⅝ = 6 ∫ dv / v⅝ = 6 ∫ v ⁻ ⅝ dv = 6 v ⁻ ⅝ ⁺ ¹ / ( - 5 / 8 + 1 ) + C =
6 v ⅜ / ( 3 / 8 ) + C = 6 ∙ 8 ∙ v ⅜ / 3 + C = 3 ∙ 2 ∙ 8 ∙ v ⅜ / 3 + C =
2 ∙ 8 ∙ v ⅜ + C = 16 ∙ v ⅜ + C