Ex 7.3, 8 - Chapter 7 Class 12 Integrals

Transcript

Ex 7.3, 8 1 − 𝑐𝑜𝑠 𝑥﷮1 + 𝑐𝑜𝑠 𝑥﷯ ﷮﷮ 1 − cos﷮𝑥﷯﷮1 + cos﷮𝑥﷯﷯﷯ We know that Thus, our equation becomes ﷮﷮ 1 − cos﷮𝑥﷯﷮1 + cos﷮𝑥﷯﷯﷯ 𝑑𝑥= ﷮﷮ 2 sin﷮2﷯﷮ 𝑥﷮2﷯﷯﷮2 cos﷮2﷯﷮ 𝑥﷮2﷯﷯﷯﷯ = ﷮﷮ sin﷮2﷯﷮ 𝑥﷮2﷯﷯﷮ cos﷮2﷯﷮ 𝑥﷮2﷯﷯﷯﷯ 𝑑𝑥 = ﷮﷮ tan﷮2﷯﷮ 𝑥﷮2﷯﷯﷯ 𝑑𝑥 = ﷮﷮ sec﷮2﷯﷮ 𝑥﷮2﷯ −1﷯﷯﷯𝑑𝑥 = ﷮﷮ sec﷮2﷯﷮ 𝑥﷮2﷯﷯﷯𝑑𝑥− ﷮﷮𝑑𝑥﷯ = tan﷮2﷯ ﷮ 𝑥﷮2﷯﷯﷮ 1﷮2﷯﷯ −𝑥+𝐶 =𝟐 𝐭𝐚𝐧﷮ 𝒙﷮𝟐﷯﷯ −𝒙+𝑪