Turito Academy

Test Prep

Global form fields

If f : R → R is continuous and differentiable function such that <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy integral subscript negative 1 end subscript superscript x end superscript blank" width="29" height="41" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«msubsup»«mo stretchy=¨false¨»∫«/mo»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/msubsup»«mrow/»«/mrow»«/math»'/>f(t) dt + f¢¢¢ (3) <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy integral subscript x end subscript superscript 0 end superscript d t equals not stretchy integral subscript 1 end subscript superscript x end superscript blank" width="86" height="43" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«msubsup»«mo stretchy=¨false¨»∫«/mo»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»0«/mn»«/mrow»«/msubsup»«mrow»«mi»d«/mi»«mi»t«/mi»«mo»=«/mo»«mrow»«msubsup»«mo stretchy=¨false¨»∫«/mo»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/msubsup»«mrow/»«/mrow»«/mrow»«/mrow»«/math»'/>t3 dt – f ¢ (1) <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAApCAYAAAArpDnNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAaPUZr5AAAAZlJREFUeNrdlzFIAlEcxo9DnESQozGEBmlqdwgJJCIkJIimiLaIiIagqSHaGxpaJKLpIBokItyOCIc2BwkJmqLBJUQaQgT7HnwHj8Mhj/sc+uAHzxPux7v3v3f/5zjJ5xkscOyCBsgLPE4F+Byfg3VHmBY4BDVHnAvQAem4N8iBK9AFA3DHdbBT5qN7BTNxRWZhP8AcOACfXJMws+AJZMAeOIu7yCOwzRuacRN4/D/NiitYv98pnShNPq6UVbqJJ8sZBOoqqlIkL9dTinbUoluKKmpRi6J5tegHDFWVFibD2fTUs1mmqKEWbVDkq0W7FF2qRTVrj5PGp6iqFj1SVFaLehRllRKXL+pQPRuPs+mqRSsU3atFmxTdTOs7dPRv3qGAorxaZL5D32pJQblrL4ESx/sUrSUtOeGNH7gjtNkrjOtYOyRWs2L65BewBeqgbx2owhTZW3sk4LWJkqLsGhyzkY+mbj1ak0XVrtGPdEIuryWe0Zhrg2nMKKWaUXSNSqzSxFNkpeV4bDQVuKraMcy78wa+eLz8U34BScpjAQB+Qm4AAAB3dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWJzdXA+PG1vPiYjeDIyMkI7PC9tbz48bW4+MDwvbW4+PG1pPng8L21pPjwvbXN1YnN1cD48L21hdGg+R6n1KgAAAABJRU5ErkJggg==" class="Wirisformula" alt="not stretchy integral subscript 0 end subscript superscript x end superscript blank" width="26" height="41" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«msubsup»«mo stretchy=¨false¨»∫«/mo»«mrow»«mn»0«/mn»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/msubsup»«mrow/»«/mrow»«/math»'/>t2 dt + f ¢¢ (2) <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy integral subscript x end subscript superscript 3 end superscript blank" width="26" height="43" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«msubsup»«mo stretchy=¨false¨»∫«/mo»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msubsup»«mrow/»«/mrow»«/math»'/>t. dt, then the value of f ¢ (4) is :

Solution for the question - if f : r r is continuous and differentiable function such thatint_(-1)^(x) f(t) dt + f (3) int_(x)^(0)dt=int_(1)^(x) t3 dt  f (1) in