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Integrals

Short Answer Type

231.

space F i n d space colon integral fraction numerator left parenthesis 2 x minus 5 right parenthesis e to the power of 2 x end exponent over denominator left parenthesis 2 x minus 3 right parenthesis end fraction d x

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232.

Find space colon integral fraction numerator straight x squared plus straight x plus 1 over denominator left parenthesis straight x squared plus 1 right parenthesis left parenthesis straight x plus 2 right parenthesis end fraction dx

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233.

Evaluate space colon space integral subscript negative 2 end subscript superscript 2 fraction numerator straight x squared over denominator 1 plus 5 to the power of straight x end fraction dx.

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234.

Find colon space integral left parenthesis straight x plus 3 right parenthesis square root of 3 minus 4 straight x minus straight x squared space end root space dx.

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235.

Find the integrating factor for the following differential equation: $straight x space log space straight x dy over dx space plus space straight y space equals space 2 logx space$

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236.

Evaluate: $integral subscript 0 superscript straight pi divided by 2 end superscript fraction numerator sin squared straight x over denominator sinx plus cosx end fraction dx.$

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237.

Evaluate $integral subscript negative 1 end subscript superscript 2 left parenthesis straight e to the power of 3 straight x end exponent plus 7 straight x minus 5 right parenthesis dx$

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238.

Evaluate:
$integral fraction numerator straight x squared over denominator straight x to the power of 4 plus straight x squared minus 2 end fraction dx$

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239.

Evaluate: $integral fraction numerator left parenthesis straight x plus 3 right parenthesis straight e to the power of straight x over denominator left parenthesis straight x plus 5 right parenthesis cubed end fraction dx$

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240.
Three schools X, Y, and Z organized a fete (mela) for collecting funds for flood victims in which they sold hand-held fans, mats and toys made from recycled material, the sale price of each being Rs. 25, Rs. 100 andRs. 50 respectively. The following table shows the number of articles of each type sold:
School/Article School X School Y School Z
Hand-held fans 30 40 35
Mats 12 15 20
Toys 70 55 75
Using matrices, find the funds collected by each school by selling the above articles and the total funds collected. Also write any one value generated by the above situation.

open square brackets table row 30 12 70 row 40 15 55 row 35 20 75 end table close square brackets space open square brackets table row 25 row 100 row 50 end table close square brackets space space space space equals space open square brackets table row cell 30 cross times 25 plus 12 cross times 100 plus 70 cross times 50 end cell row cell 40 cross times 25 plus 15 cross times 100 plus 55 cross times 50 end cell row cell 35 cross times 25 plus 20 cross times 100 plus 75 cross times 50 end cell end table close square brackets space space space space equals open square brackets table row 5450 row 5250 row 6625 end table close square brackets space equals space open square brackets table row straight X row straight Y row straight Z end table close square brackets

The funds collected by X = Rs.5450, Y= Rs. 5250, Z = Rs. 6625
Total funds collected = Rs. 17325
Value generated: team work.

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