text: Class 12
  MATHS
  Definite Integration
  
  # Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx
  
  Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
  
  Updated On: 26-9-2020
  
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  Very Important Questions
  
  I=(b-a)int_(0)^(1)f((b-a)x+a)dx <br> Let (b-a)x+a=t <br> impliesdx=(dt)/((b-a)) <br> impliesdx=(dt)/((b-a)) <br> Also when x=0 then t=a an x=1 then t=b <br> :.I=(b-a)int_(a)^(b)f(t)(dt)/((b-a)) <br> =int_(a)^(b)f(t)dt <br> =int_(a)^(b)f(x)dx (Change of dummy variable)
explanation: The text extract contains a math question and its solution. The question asks to prove a property of definite integrals, and the solution is provided step by step.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Class 12
  MATHS
  Definite Integration
  
  # Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx
  
  Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
  
  Updated On: 26-9-2020
  
  Apne doubts clear karein ab Whatsapp par bhi. Try it now.
  
  Watch 1000+ concepts & tricky questions explained!
  
  66.0 K+
  
  3.3 K+
  
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  1:59
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  5.5 K+
  
  111.1 K+
  
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  33.0 K+
  
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  2.3 K+
  
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  34.5 K+
  
  5:11
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  78.4 K+
  
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  57.0 K+
  
  83.1 K+
  
  3:23
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  12.4 K+
  
  248.3 K+
  
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  1.4 K+
  
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  34763
  
  3.2 K+
  
  64.1 K+
  
  4:37
  96594200
  
  6.7 K+
  
  24.3 K+
  
  3:12
  
  Very Important Questions
  
  I=(b-a)int_(0)^(1)f((b-a)x+a)dx <br> Let (b-a)x+a=t <br> impliesdx=(dt)/((b-a)) <br> impliesdx=(dt)/((b-a)) <br> Also when x=0 then t=a an x=1 then t=b <br> :.I=(b-a)int_(a)^(b)f(t)(dt)/((b-a)) <br> =int_(a)^(b)f(t)dt <br> =int_(a)^(b)f(x)dx (Change of dummy variable)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract contains a math question and its solution. The question asks to prove a property of definite integrals, and the solution is provided step by step.
  
  Label: question-and-answer