Evaluate the following: dttt∫dt3t-2t2

प्रश्न

Evaluate the following:

`int "dt"/sqrt(3"t" - 2"t"^2)`

योग

उत्तर

Let I = `int "dt"/sqrt(3"t" - 2"t"^2)`

= `int "dt"/sqrt(-2("t"^2 - 3/2 "t"))`

= `1/sqrt(2) int "dt"/sqrt(-("t"^2 - 3/2 "t" + 9/16 - 9/16))` ....[Making perfect square]

= `1/sqrt(2) int "dt"/sqrt(-[("t" - 3/4)^2 - 9/16])`

= `1/sqrt(2) int "dt"/sqrt(9/16 - ("t" - 3/4)^2)`

= `1/sqrt(2) int "dt"/sqrt((3/4)^2 - ("t" - 3/4)^2)`

= `1/sqrt(2) * sin^-1 ("t" - 3/4)/(3/4) + "C"`

= `1/sqrt(2) sin^-1 (4"t" - 3)/3 + "C"`

Hence, I = `1/sqrt(2) sin^-1 ((4"t" - 3)/3) + "C"`

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Evaluation of Definite Integrals by Substitution

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 15 Q 14 Q 16

अध्याय 7: Integrals - Exercise [पृष्ठ १६४]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12

अध्याय 7 Integrals
Exercise | Q 15 | पृष्ठ १६४

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Evaluation of Definite Integrals by Substitution

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