Example 1 - Write anti derivative using inspection - Examples

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Example 1 Write an anti derivative for each of the following functions using the method of inspection: (i) cos⁡2𝑥 We know that 𝑠𝑖𝑛 𝑥﷯﷮′﷯=𝑐𝑜𝑠 𝑥 𝑠𝑖𝑛 2𝑥﷯﷮′﷯=𝑐𝑜𝑠 2𝑥.2 𝑠𝑖𝑛 2𝑥﷯﷮′﷯=2𝑐𝑜𝑠 2𝑥 𝑠𝑖𝑛 2𝑥﷯﷮′﷯﷮2﷯=𝑐𝑜𝑠 2𝑥 Hence Anti Derivative of is 𝟏﷮𝟐﷯ 𝒔𝒊𝒏 𝟐𝒙﷯ Example 1 Write an anti derivative for each of the following functions using the method of inspection: (ii) 3 𝑥﷮2﷯+4 𝑥﷮3﷯ We know that Adding (1) and (2) 𝑥﷮3﷯﷯﷮′﷯+ 𝑥﷮4﷯﷯﷮′﷯=3 𝑥﷮2﷯+4 𝑥﷮3﷯ Hence Anti derivative of is 𝒙﷮𝟑﷯+ 𝒙﷮𝟒﷯ Example 1 Write an anti derivative for each of the following functions using the method of inspection: (iii) 1﷮𝑥﷯, 𝑥≠0 We know that log﷮𝑥﷯﷯﷮′﷯= 1﷮ 𝑥﷯ Hence Anti derivative of is 𝟏﷮𝒙﷯

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